Atom-Based Electromagnetic Field Sensing Element and Measurement System

ABSTRACT

Methods and apparatus for sensing or measuring an electromagnetic field. The method entails excitation into a distribution of Rydberg states of atoms of a gas occupying a test volume coextensive with the electromagnetic field. Transmission along a path traversing the test volume of at least one probe beam of electromagnetic radiation is measured at one or more frequencies overlapping a spectral feature, and a physical characteristic of the electromagnetic field is derived on the basis of variation of the spectral feature. In various embodiments, the electromagnetic field may be place in interferometric relation with another electromagnetic field. Time-varying electric field amplitude, frequency, phase and noise spectral distribution may be measured, and thus AM and FM modulated fields, as well as magnetic fields of about 1 Tesla. The apparatus for measuring the electromagnetic field may be unilaterally coupled to a probe field and detector or array of detectors.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 17/087,011, filed Nov. 2, 2020,which in turn is a continuationof U.S. patent application Ser. No. 16/222,384, filed Dec. 17, 2018,which in turn claims the priority of U.S. Provisional Application No.62/607,034, filed Dec. 18, 2017, and of U.S. Provisional Application No.62/727,764, filed Sep. 6, 2018. Each of the above applications is herebyincorporated herein by reference in their entirety.

GOVERNMENT RIGHTS

This invention was made in part with Government support under ContractNo. W911NF-17-C-0007, awarded by the Defense Advanced Research ProjectsAgency (DARPA) and the US Army. The Government may have rights in someaspects of the invention.

FIELD OF INVENTION

The present invention relates to an atom-based field sensing element andmeasurement system and methods, and, more particularly, to an element,system and methods that employ Rydberg atoms to measure, receive orimage RF field amplitude, polarization, or phase, modulated RF signals,incoherent RF or RF noise, and to perform continuous-frequency RF fielddetection.

BACKGROUND OF THE INVENTION

Atoms with a quasi-free electron in a high-lying Rydberg state(characterized by a high principal quantum number, typically n>20)exhibit large polarizabilities and electric dipole moments that scalewith principal quantum number n as ˜n⁷ and ˜n², respectively, renderingthem exquisitely sensitive to electric fields. In accordance with theconvention of the present text, states of an atom which are not Rydbergstates may be referred to herein as “low-lying states”.

The concept of applying the spectroscopic response of Rydberg states inatomic vapors to the measurement of electric fields has been known atleast since Mohapatra et al., “Rydberg States using ElectromagneticallyInduced Transparency,” Phys. Rev. Lett., vol. 98, 113003 (2007), whichis incorporated herein by reference. Earlier work relating to atom-basedfield sensing, all in the prior art, is the subject of U.S. Pat. No.9,970,973, to Anderson et al., hereinafter, “the Anderson '973 Patent,”incorporated herein by reference, as well as in references citedtherein. More particularly, Floquet methods have previously beenestablished as a suitable means to model Rydberg-atom microwave spectrain vapor cell experiments, as shown, for example in Anderson etal.,“Two-photon microwave transitions and strong-field effects in aroom-temperature Rydberg-atom gas,” Phys. Rev. A, vol. 90, 043419(2014), incorporated herein by reference.

Electromagnetically induced transparency (EIT) is a quantum interferenceprocess in which two excitation pathways in a three-level atomic systemdestructively interfere and produce an increase in the transmission of aprobe laser beam. In the Rydberg-EIT cascade scheme, depicted, forexample, in FIG. 8B, the transparency is formed by a coherentsuperposition of the ground and Rydberg states. Rydberg-EIT has beenimplemented in both cold atomic gases and in room-temperature vaporcells. It has been widely used as a nondestructive optical detectiontechnique for Rydberg spectra, quantum information processing, andmeasurements of both weak and strong microwave electric fields. AC Starkshifting of Rydberg levels using electrodes in a vapor cell is discussedby Bason et al., “Enhanced electric field sensitivity of rf-dressedRydberg dark states,” New J. Phys., vol. 12, 065015 (2010), which isincorporated herein by reference.

As the term is used herein, the word “sensor” shall refer to any devicethat detects or measures a physical quantity and may exclude wiring orwaveguides that couple electrical or electromagnetic energy to or fromthe sensor, as well as controllers or processors used with the sensor.The term “monolithic sensor,” as the term is used herein, refers to asensor, the entirety of which is embodied on a singular substrate orwhose components are permanently connected to form a single physicaldevice. Examples of connections include microfabrication, fusing, anodicbonding, and gluing. To the best of the knowledge of the inventorshereto, a monolithic Rydberg sensor has never been suggested.

No method of Rydberg spectroscopy hitherto suggested, however, has everbeen suited to measuring a phase of an electromagnetic field (relativeto a fiducial phase reference). To that lacuna, among others,embodiments of the invention described below are addressed.

To realize a practical atom-based RF sensing, measurement, or imagingdevice, a suitable sensing element is required. All prior art sensingelements, described or suggested in earlier work, had limitationsimposed by physical principles that were overcome by virtue of insightsdescribed below in accordance with the present invention. Prior artsensing elements are taught, for example, by Anderson et al., “Opticalmeasurements of strong microwave fields with Rydberg atoms in a vaporcell,” https://arxiv.org/pdf/1601.02535.pdf , (11 Jan. 2016), which isincorporated herein by reference.

Other teachings of atom-based electromagnetic field sensing may be foundin Gordon et al., “Millimeter Wave Detection via Autler-Townes Splittingin Rubidium Rydberg Atoms,” https://arxiv.org/pdf/ 1406.2936.pdf , (11Jun. 2014), and in Simons et al., “Using frequency detuning to improvethe sensitivity of electric field measurements via electromagneticallyinduced transparency and Autler-Townes splitting in Rydberg atoms,”Appl. Phys. Lett., vol. 108, 174101 (2016), both of which publicationsare also incorporated herein by reference.

Performance limitations of existing Rydberg electromagnetically inducedtransparency (EIT) techniques include:

(1) Low sensitivity; the highest field sensitivity demonstrated to dateis at the 1 mV/m level, limited primarily by EIT linewidths.Furthermore, this sensitivity level has only been achieved by monitoringsmall changes in the EIT peak line shape. Unlike measuring Rydbergenergy-level spitting directly, where the field is traceable tofundamental constants and invariable atomic parameters, extracting theRF electric field from a detailed EIT line shape analysis requires arelatively complex model that depends on experimental parameters such aslaser beam powers and vapor pressures, thereby precluding an absolutefield measurement and making it unreliable in everyday operation. Todate, the most sensitive measurement sensitivity in the prior art, ashot-noise limited sensitivity of about 3 μV/cm/ Hz^(1/2), has beendemonstrated in work of Kumar et al., “Rydberg-atom basedradio-frequency electrometry using frequency modulation spectroscopy inroom temperature vapor cells,” Opt. Express, vol. 25, 284263 (21 Jan.2017), an improvement of half an order of order of magnitude oversensitivity reported earlier in Fan et al., “Effect of Vapor CellGeometry on Rydberg-Atom-Based Measurements of Radio-Frequency ElectricFields,” Phys. Rev. Appl., 044015 (2015), both of which papers areincorporated herein by reference. The latter work exploits minuteRF-induced EIT enhancement of Rydberg-EIT lines by weak, resonant RFfields, a method expected to be somewhat unreliable in everydayfield-measurement operation, because the minute changes depend on manydetails, such as laser powers and cell pressure. More robust means toenhance the sensitivity are desired.

(2) Inability to measure RF fields over a continuous frequency range. Inweak RF fields, the method is limited to measurements of RF fields thatare resonant with dipole-allowed transitions between Rydberg states.Weak RF fields that are off- and far-off-resonance from any transitioncannot be measured easily, if at all.

(3) RF polarization measurements currently require a complex analysis ofthe atomic spectra.

(4) All prior art Rydberg-EIT measurements have necessarily been fieldamplitude measurement, while information on the phase of the RF fieldhas never been possible to obtain in part because of physicalconstraints discussed herein.

(5) The form factor of measurement apparatuses used to date for RydbergEIT measurements have necessarily require large components, assembliesthat are not portable or have a large dielectric footprint, therebyprecluding the ability to perform measurements in many practicalapplications or to be integrated into existing RF measurement andtransmission systems.

(6) Prior to the invention described herein below, Rydberg EITtechniques have served solely for measurement of coherent fields. Priormethods were incapable of measuring either incoherent fields or noise.

An RF measurement method employing Rydberg EIT in vapor cells typicallyemploys counter-propagation of laser beams through the atomic vapor toaccount for Doppler-shifts of the spectroscopic laser beams in thethermal atomic sample. This aspect has, to-date, posed a challenge inthe implementation of Rydberg EIT in vapor cells in practical sensordesigns for applications because it requires the laser beams to enterand exit the cells from opposing sides, either via free-spacepropagation or optical fibers on either side of the cell. This can leadto a sensor head with a large dielectric footprint and size that isundesirable for measurement applications. Further, for extensions tomulti-pixel sensor arrays, entry of the optical beams from oppositesides of the cells can limit pixel packing density and resolutionachievable in an array.

While single-sided optical coupling into vapor cells has been discussed,for example, in the context of an atomic magnetometer by George et al.,“Pulsed high magnetic Field Measurement via a Rubidium Vapor Sensor,”https://arxiv.org/pdf/1704.00004.pdf , (31 Mar. 2017), which isincorporated herein by reference, separate fibers are employed there forinput and output beams, and beams of the same or similar wavelength.Moreover, in the prior art, the probe beam always enters on one side ofa vapor cell and exits on a different side.

While most of the matter in the observable universe exists in the plasmastate, measurement or inference of characteristics of an electric fieldwithin a region of plasma poses particular challenge to science unlesscollective motion of the plasma may be observed, or unless a physicalprobe can be inserted into the plasma. An example of the formertechnique is the inference of radial electric fields in a tokomak,inferred from poloidal rotation velocities. Absent either of theseprobing modalities, certain assumptions need to be made where atomicprobes are used. For example, where an intensity ratio of spectral bandsof nitrogen is used, as discussed by Paris et al., “Intensity ratio ofspectral bands of nitrogen as a measure of electric field in plasmas,”J. Phys. D, vol. 38, pp. 3894-99 (2005), incorporated herein byreference, calculations require that the nitrogen molecules bepredominantly excited from the ground state directly by electron impact.

To date, optical diagnostic techniques for measurements of plasma fieldsprimarily involve the measurement of Stark shifts in plasma molecules byway of emission and absorption spectroscopy, laser-induced fluorescence,and Raman spectroscopy. While existing methods afford passivenon-intrusive measurements, they may also require a priori knowledge ofthe optical absorption or emission spectra of the plasma constituents.This can make it difficult to distinguish collective plasma phenomena ofinterest from few-body processes involving constituent plasma particlesin the diagnostic readout. It also requires the customization of adiagnostic tool specific to the plasma type under study, precluding ageneralized technique capable of performing diagnostics on differentplasma systems. Along these lines, some plasmas are expected to haveemission profiles at frequencies and emission strengths that aredifficult to detect using conventional detectors and spectrometers. WeakIR emissions from vibrational transitions in plasma constituents, forexample, may in some instances provide useful information but detectorsrequired for measuring these low IR intensity levels have not beenreadily available. Due to these restrictions, applications may requirethat the plasma be engineered with certain atomic/ionic particles toimplement well-characterized optical diagnostics. This can pose asignificant drawback in fundamental plasma studies, where the nature ofthe plasma is itself the subject of study.

Insofar as a priori knowledge of the aforesaid sort is not alwaysavailable, science has awaited a more universal modality for remotemeasurement of electric fields within a plasma. Such a modality isdescribed in detail below in accordance with an embodiment of thepresent invention.

Probes for high-resolution sensing, measurement and calibration ofstrong magnetic fields in the 1-100 Tesla range are becomingincreasingly important in research and development, production, andmaintenance of strong magnet systems in variety of industries. However,no atomic vapor or Rydberg-EIT system has provided for measurement ofsuch fields, enabled, for the first time, by virtue of the inventiondescribed below. The maximum magnetic field strength that may bemeasured based on a model of Rydberg atoms using Zeeman splitting ofhyperfine levels by Rydberg EIT analysis as previously practiced is atmost ˜10³ Gauss. Measurement of stronger magnetic fields requires a newstratagem, as described herein in accordance with the present invention.

SUMMARY OF THE INVENTION

In accordance with an embodiment of the present invention, a method isprovided for sensing or measuring a first electromagnetic field. Themethod has steps of:

exciting, into a distribution of Rydberg states, atoms of a gasoccupying a test volume coextensive, at least in part, with the firstelectromagnetic field;

structuring the first electromagnetic field by placing it ininterferometric relationship with at least one other electromagneticfield;

measuring transmission along a path traversing the test volume of atleast one probe beam of electromagnetic radiation at one or morefrequencies overlapping a spectral feature of the atomic gas; and

on the basis, at least, of a change in the spectral feature, deriving aphysical characteristic of the first electromagnetic field.

In accordance with other embodiments of the invention, the gas may be anatomic vapor, and atoms of the atomic vapor may be chosen from a groupof atoms including rubidium, cesium and other alkalis. The step ofexciting atoms into a distribution of Rydberg states may compriseoptically exciting the atoms into a distribution of Rydberg states andat least one of electromagnetically induced transparency andelectromagnetically induced absorption.

In accordance with further embodiments of the invention, the change inthe spectral feature may include Autler-Townes splitting, and thephysical characteristic of the first electromagnetic field may be fieldamplitude.

The first electromagnetic field may be monochromatic, and the physicalcharacteristic of the first electromagnetic may be its phase relative toa fiducial phase.

In accordance with other embodiments of the present invention,structuring the first electromagnetic field may include modulation ofthe electromagnetic field prior to the step of measuring. Modulation maybe at least one of frequency-, amplitude-, and step-modulation.

In still another embodiment of the present invention, the distributionof Rydberg states may include at least one pair of states with anon-zero dipole moment for the interaction between an atom and aradio-frequency field.

In accordance with yet a further embodiment of the present invention,there may be additional steps of:

calculating predetermined Rydberg atomic energy levels or Rydberg-EITspectra in a presence of an incoherent RF noise field present in orconstituting the first electromagnetic field;

propagating light into an atomic vapor cell;

measuring spectral features with the light propagated through the atomicvapor cell;

identifying a matched spectrum; and

deriving an attribute of the incoherent RF noise field.

In accordance with another embodiment of the present invention, theremay be additional steps of:

calculating predetermined atomic energy levels or spectra for atoms in afirst electromagnetic field that is identical to a strong static orlow-frequency magnetic field;

propagating at least one other electromagnetic field as an optical probeinto an atomic vapor cell;

measuring spectral features of the light propagated through the atomicvapor cell;

identifying a matched spectrum; and

deriving a physical property of the strong magnetic field.

The light may be amplitude or frequency modulated in conjunction withlock-in detection at the modulation frequency or a multiple of thatfrequency, and the predetermined atomic energy levels or spectra may befor low-lying atomic states.

In accordance with another aspect of the present invention, a monolithicsensor is provided for detecting and/or measuring a parametercharacterizing an electromagnetic field. The sensor has an atomic vaporcontained within an enclosure, a source of excitation for exciting atomsof the atomic vapor into a distribution of Rydberg states, and at leastone waveguide for coupling a probe beam or more beams into the atomicvapor and for collecting the probe beam after interaction of the probebeam with the atomic vapor.

In accordance with other embodiments of the invention, the at least onewaveguide may be an optical fiber. At least one of the at least onewaveguide may couple radiation from both the source of excitation andthe probe beam into the atomic vapor. The enclosure may include adielectric material or a glass vapor cell. The enclosure may becompartmented, and, more particularly, may be linearly or arealycompartmented.

In further embodiments, a distinct probe beam may be coupled into eachof an array of compartments, such as via an array of optical elements,and may be collected after interaction with the atomic vapor and coupledto a detector element via the array of optical elements. The enclosuremay include a light-absorbing surface, and may also have a temperatureregulator.

In accordance with a further aspect of the present invention, aunilaterally-coupled monolithic sensor is provided for detecting and/ormeasuring a parameter characterizing an electromagnetic field. Theunilaterally-coupled monolithic sensor has an atomic vapor containedwithin a dielectric enclosure and a source of excitation for generatingan excitation beam for exciting atoms of the atomic vapor into adistribution of Rydberg states. Additionally, the unilaterally-coupledmonolithic sensor has a first prism for coupling the excitation beaminto the atomic vapor and for coupling a probe beam out of the atomicvapor and a second prism for coupling the probe beam into the atomicvapor. The excitation beam and the probe beam may be incident on therespective first and second prisms in substantially parallel directions.

In yet a further aspect of the present invention, a sensor is providedfor detecting and/or measuring a parameter characterizing anelectromagnetic field. The sensor has at least one of a material or astructure for conditioning an electromagnetic field, and an atomic vaporcontained within an enclosure disposed within the conditioning materialor structure. The sensor also has a source of excitation for excitingatoms of the atomic vapor into a distribution of Rydberg states, adetector for detecting a probe beam after traversal of the atomic vaporand for generating a detector signal, and a processor for deriving aparameter characterizing the electromagnetic field based at least on thedetector signal.

In other embodiments, the material or structure for conditioning anelectromagnetic field may be an RF resonator or a waveguide. It may alsobe a metamaterial.

The material or structure for conditioning an electromagnetic field mayinclude an antenna or one or more electrodes. The material or structuremay be conductive and may condition the electromagnetic field byconversion of a current or voltage signal into an electromagnetic fieldwithin an atomic vapor cell. An attribute of the current or voltagesignal may be derived from the detector signal.

In other embodiments of the invention, the source of excitation forexciting atoms of the atomic vapor into a Rydberg state may have one ormore light beams to establish an electromagnetically inducedtransparency or electromagnetically induced absorption in the atomicvapor. The enclosure containing the atomic vapor may be a glass vaporcell.

In yet other embodiments of the invention, the material or structure forconditioning an electromagnetic field may include a filter or reflectorfor electromagnetic fields that are entering or exiting the atomic vaporenclosure. The detector may be used to detect an electromagnetic fieldgenerated by the excitation of and emission from the atomic vapor. Theelectromagnetic field may be associated with at least one of a standingelectromagnetic wave and a traveling electromagnetic wave.

In accordance with another aspect of the present invention, a sensor isprovided for detecting and/or measuring a parameter characterizing anelectromagnetic field. The sensor has an atomic vapor contained withinan enclosure that, in turn, has a light-absorbing surface. The sensoralso has a source of a heating beam incident upon the light-absorbingsurface as well as a source of excitation for exciting atoms of theatomic vapor into a distribution of Rydberg states. The sensor also hasa detector for detecting a probe beam after traversal of the atomicvapor and for generating a detector signal, and a processor for applyingthe heating beam to the light-absorbing surface in such a manner as toregulate a temperature characterizing the atomic vapor.

In further embodiments of the invention, the light-absorbing surface maybe a film, a polymer or a glass.

In accordance with another aspect of the present invention, a method isprovided for measuring an electric field within a region of a plasmacontained within an enclosure. The method has steps of:

incorporating tracer particles of a specified species into the plasma;

exciting the tracer particles into a specified Rydberg state;

applying at least a probe beam and coupler beam to derive an EITtransmission spectrum of the plasma; and

comparing the EIT transmission spectrum of the plasma with a spectralmodel to infer the electric field with the region of the plasma on thebasis of at least one of field-induced spectral shape changes andfield-induced spectral shifts.

In accordance with more embodiments of the invention, the method mayhave a further step of applying a magnetic field or RF field to theplasma. The tracer particles may be atoms, including, more particularly,Rubidium atoms. The method may also include generating the tracerparticles from a cold-atom source.

DESCRIPTION OF DRAWINGS

The foregoing features of the invention will be more readily understoodby reference to the following detailed description, taken with referenceto the accompanying drawings, in which:

FIG. 1 schematically depicts a single-sided optically-coupled RF sensingelement in accordance with an embodiment of the present invention.

FIG. 2A shows an EIT spectrum of the 30D Rydberg state of ⁸⁷Rb obtainedusing a pen-like retro-EIT configuration in accordance with anembodiment of the present invention.

FIG. 2B shows a single-sided atomic vapor sensor in which excitation andprobe beams are coupled to a vapor cell via prisms, in accordance withan embodiment of the present invention.

FIG. 3 shows a microwave imaging array comprised of single-side-coupledindividual vapor-cell sensor elements, in accordance with an embodimentof the present invention.

FIG. 4A shows a calculation of an RF-field enhancement factor along theaxis of a tip of 125 um diameter for several frequencies, in accordancewith an embodiment of the present invention. FIG. 4B shows the skindepth associated with a conducting tip.

FIGS. 5A and 5B show a type of hybrid atom-cavity structure inaccordance with an embodiment of the present invention.

FIG. 6 shows a calculation of electric field in the hybrid atom-cavitystructure shown in FIGS. 5A-5B for a near-resonant 4 GHz incident RFfield of 1 V/m.

FIGS. 7A-7D show a hybrid atom-resonator device, in accordance with anembodiment of the present invention. FIG. 7A shows a resonatorelectrode/cavity inside a spectroscopic cell; FIG. 7B is a top view ofthe resonator showing the ceramic pins for electrode alignment andstabilization; FIG. 7C is a side view of the resonator with a glassspacer and gap indicated; and FIG. 7D shows the resonatorelectrode/cavity structure inside a rubidium vapor cell with wire leadsconnected for external voltage/current control, or to ground/short theelectrodes.

FIG. 8A shows an experimental setup for measurement of fieldcharacteristics in accordance with an embodiment of the presentinvention, while FIG. 8B shows the pertinent Rydberg EIT energy leveldiagram.

FIGS. 9A-9D demonstrate hybrid atom-cavity field enhancement inaccordance with an embodiment of the present invention. FIG. 9A plots ameasured 31S Rydberg EIT spectrum as a function of RF/microwavefrequency at a fixed −10 dBm injected power. FIG. 9B plots a calculatedStark map centered on the 31S_(1/2) Rydberg state for an appliedroot-mean-square electric field E_(RMS). FIG. 9C plots microwave E_(RMS)versus frequency obtained using FIGS. 9A and 9B, while FIG. 9D plotsmeasured EIT lines for 2.5 and 4.35 GHz microwaves, respectively.

FIGS. 10A and 10B show side and end views of a field measurement systemwith an atomic vapor cell internal to a waveguide, in accordance with anembodiment of the present invention.

FIG. 11A shows experimental 31S Rydberg AC-Stark shifts as a function ofapplied microwave frequency at a fixed injected power for differentangular positions ⊖ relative to a vertical axis. FIG. 11B plotsmicrowave electric field at 4.35 GHz as a function of ⊖ for the datashown in FIG. 11A.

FIG. 12A shows results of calculations of electric field amplitude, andFIGS. 12B-12D, of electric field vector direction, in the hybridatom-cavity structure of FIGS. 7A-7D, in accordance with an embodimentof the present invention.

FIGS. 13A and 13B show experimental and calculated DC Stark maps,respectively, of the 30D Rydberg state for an applied DC electric field.

FIG. 14 depicts Floquet calculation of AC Stark shifts of the rubidium47S and 47P levels in a 100 MHz RF field.

FIG. 15 plots an RF intensity and electric field calibration on therubidium 47S state.

FIG. 16 plots measured EIT spectra of the 47S state versus microwavefrequency detuning from 37.51663492 GHz) at a fixed −14 dBI microwaveintensity (separate calibration) for 4 different injected RF powers.

FIG. 17 plots the center of the measured avoided crossing as a functionof applied RF electric field for a series of values out to about 200V/cm.

FIG. 18A shows simulated electric field generated inside four differentsplit-ring cavity structures for a 1 V/m incident field as a function ofapplied frequency. FIG. 18B illustrates a measurement channel within thegap of the split-ring cavity structure, in accordance with an embodimentof the present invention. FIGS. 18C and 18D show simulated resonancecurves for split-ring resonators with geometries that lead to resonancesin the vicinity of 100 GHz.

FIGS. 19A and 19B show an IR-glass capsule 1901 enclosing a 4 mm innerdiameter atomic vapor cell 1903. FIG. 19C shows an all-optical heatingtest platform.

FIG. 20A schematically depicts a sensing element backend and operatingprinciple for phase-sensitive measurements of RF electric fields, inaccordance with an embodiment of the present invention. FIG. 20B depictsa quantum mechanical level scheme and optical/RF excitation pathwaysused in the phase-sensitive RF electric-field measurement.

FIG. 21 is a flowchart depicting steps in the Rydberg-EIT measurement ofattributes of a magnetic field, made possible for the first time inaccordance with an embodiment of the present invention.

FIG. 22 is a flowchart depicting steps in the Rydberg-EIT measurement ofattributes of RF noise over a specified spectral range, made possiblefor the first time in accordance with an embodiment of the presentinvention.

FIGS. 23A-23C schematically depict probing electromagnetic fields withina plasma employing EIT of Rydberg atom tracers, in accordance with anembodiment of the present invention.

FIGS. 24A-24C schematically depict measuring a strong magnetic fieldusing saturation absorption spectroscopy of a two-level Rydberg quantumsystem, in accordance with an embodiment of the present invention.

FIGS. 25A-25C schematically depict measuring a strong magnetic fieldusing saturation absorption spectroscopy of a three-level Rydbergquantum system, in accordance with an embodiment of the presentinvention.

FIG. 26A schematically depicts a hybrid atom-based opticalRF-power/voltage transducer and sensor in accordance with an embodimentof the present invention, and FIG. 26B shows plots of signals obtainedat various levels of voltage applied across electrodes of the transducerand sensor.

FIG. 27A schematically depicts an atomic vapor-cell compartment withopposing windows for wavelength-selective transmission ofelectromagnetic waves, in accordance with an embodiment of the presentinvention. FIG. 27B shows an image of the atomic vapor-cell compartmentof FIG. 27A.

EMBODIMENTS OF THE INVENTION

Definitions: The following terms shall have the meanings indicated,unless otherwise dictated by context:

Certain embodiments of the present invention relate to an atom-basedfield sensing element that may also be referred to herein, synonymously,as a “sensing element,” a “field sensing element,” and as a “sensor.”

“Conditioning” shall, herein and in any appended claims, refer to theconfinement, guiding, manipulation, or filtering of an electromagneticfield or a physical attribute of the EM field including its mode,electric field amplitude, polarization, frequency, phase, and spectralcontent.

The term “enhancement,” as it refers to an electromagnetic wave, shallbe defined as the conditioning of that electromagnetic wave in such amanner as to increase the value of any physical attribute of theelectromagnetic wave.

A “monochromatic field” shall refer either to a static field or to anelectromagnetic field characterized by a range of frequencies no greaterthan 1% of a central frequency.

An electromagnetic field shall be referred to as “structured” if andonly if it is a monochromatic field and is in an interfering relationwith at least one other electromagnetic field. Thus, to “structure” anelectromagnetic field is to place the field in interferometricrelationship with one or more other electromagnetic fields.

An atom-based field sensing element shall be referred to herein as“integrated” if and only if it contains at least one material or astructure that acts to condition an RF field, where the term “condition”is as defined above. The RF field that is conditioned may be referred toherein as an “RF field of interest.”

As used herein, the word “distribution,” when referring to a set,whether continuous or discrete, shall include the case of a singleelement. Thus, a distribution of atomic population among Rydberg states,for example, encompasses a single state, as well.

As used herein, in a spectrum, which term refers herein to any functionof frequency ν, a “spectral feature” shall refer to the behavior of thatfunction over a defined contiguous frequency subdomain wherein values ofthe function at the boundaries of the subdomain constitute local minimaor maxima of the function.

“Splitting” of a spectral feature shall refer to diminution of a localmaximum of the function due to a physical effect, causing the appearanceof two new local maxima, one at a frequency above that of the originallocal maximum, and one at a frequency below that of the original localmaximum. The term “splitting,” where appropriate in context, may alsodesignate the difference in frequency between the loci of the new localmaxima that appear in place of the original local maximum.

The term “electromagnetic encompasses both DC and AC fields.

“RF” may refer synonymously herein to “microwave,” “millimeter-wave,”“terahertz,” or any electromagnetic radiation with frequency from aboveDC to THz.

A magnetic field shall be designated as “strong” if it exceeds ˜10⁻³Tesla (10 G), at which point the m-degeneracy of some atomic hyperfinelevels, broken by the magnetic field, begins to transition from theweak-field (linear Zeeman) regime into the Paschen-Back regime.

“Electromagnetically induced transparency” (EIT) refers to a physicalphenomenology in which coherent optical fields tuned to interact with(at least) three states of an optical system give rise to transparencyat a wavelength corresponding to an otherwise absorbing quantumtransition in a medium. The physics and terminology of EIT are reviewedby Marangos, “Topical review: Electromagnetically induced transparency,”J. Mod. Opt., vol. 45, pp. 471-503 (1998), which is incorporated hereinby reference.

A “dielectric,” as the term is used herein, is defined as a material orsubstance that transmits electric force without conduction; aninsulator.

An Atom-Based Electromagnetic Field Sensing Element and MeasurementSystem

In accordance with certain embodiments of the present invention, asingle-sided optically-coupled RF sensing element (otherwise referred toherein as a “sensor” and as a “pen-like configuration”) is provided, anddesignated generally by numeral 100 and is described with reference toFIG. 1. The pen-like linear sensor design depicted in FIG. 1 affords theuse of a single entrance port 102 to fiber-optically couple the requiredlaser beams 103, 104 into and out of the vapor cell volume 108 containedwithin enclosure 106, otherwise referred to herein as a “vapor cell” oran “atomic vapor cell.” Vapor cell volume 108 contains an atomic ormolecular gas. A region of gas within vapor cell volume 108 that isprobed by beams 103 and 104 may be referred to herein, and in anyappended claims, as a “test volume.”

With sensor 100 entering an active measurement volume 110 from a singleside, the configuration of FIG. 1 leaves the active measurement volume110 unobstructed with respect to incident RF/microwave fields 112 fromall sides except one. In the implementation depicted in FIG. 1,linearly-polarized probe 103 and coupler 104 beams are sent through asingle polarization-maintaining fiber 120 and collimated by a lens 122to a full-width-at-half-maximum (FWHM) of approximately 200 μm in vaporcell 106. The probe and coupler beams 103, 104 co-propagate through theatomic vapor cell 106, where the probe 103 is then selectivelyretro-reflected back through the cell by a short-pass dichroic mirrorcoating 130 while the coupler passes through and is blocked by a thindielectric absorber beam block 132. The retro-reflected probe beam 134retraces its path, overlapping the outgoing coupler beam, and isre-coupled back into fiber 120 by lens 122. A quarter wave plate 140positioned before the retro-reflection (between the lens and vapor cellin FIG. 1), ensures that the linearly polarized in-going probe beam isrotated by 90 degrees on the retro-reflected out-going beam so that itcan be selectively split off with a polarization-selective element (notshown) for readout after the polarization-maintaining (PM) fiber.

Sensor 100 as depicted in FIG. 1 may provide several advantages incomparison to other implementations of vapor-cell EIT that preceded thepresent invention. First, the linear single-sided design allows forsmall, low-profile probe tips and sensor elements that have a smalldielectric footprint. The design also eliminates the need for anyoptical elements to redirect the optical beams out of the fiber and intothe cell. Utilizing a single lens for input and output coupling oflarger beam diameters as compared to typical implementations of vaporcell EIT may advantageously improve the measurement precision andsensitivity by affording less interaction-time broadening and therewithhigher achievable spectroscopic resolution, as well as improvedoperational stability by reducing the device sensitivity to misalignmentby back-coupling the readout probe beam into the same fiber.

FIG. 2A shows an EIT spectrum, designated generally by numeral 200, ofthe 30D Rydberg state of ⁸⁷Rb using the pen-like retro-EIT configuration100 of FIG. 1. Single-sided EIT configurations may be referred to hereinas “retro-EIT configurations.” The splitting of fine-structure features204 is evident. Internal reflections of the coupler beams 104 from theinner cell walls lead to a duplicate EIT spectrum 202. The spectra aretaken without lock-in detection of the signal of a Si photodiode.

The duplicate spectrum 202 is blue-shifted from the primary EIT line 200by an amount equal to the frequency detuning of the probe 103 relativeto velocity v=0 atoms at the center of the Doppler profile. Duplicatespectra due to internal reflections in vapor cells are commonly observedin vapor-cell EIT experiments. These can be avoided by placing the cellat an angle from normal incidence of the EIT beams or having the cellwindows at an angle relative to the incident optical beam.

FIG. 2B shows an embodiment of sensing element, designated generally bynumeral 230, with single-sided fiber coupling through a rubidium vaporcapsule 232. An implementation of a sensing element in accordance withanother embodiment of the present invention, with a first prism 212 andsecond prism 214 redirecting single-sided fiber-coupled excitation beam216 and a single-sided fiber-coupled probe beam 218 into vapor capsule232. Prisms 212 and 214 are couple to respective fibers guiding beams216 and 218 by lenses 235.

In accordance with other embodiments of the present invention, thesingle-sided optically-coupled vapor-cell RF/microwave sensing elementmay be extended to multi-sensor arrays, where the single-sided couplingof an array of cells is achieved collectively using large single beamsfor the coupler and probe that impinge on a microarray of lenses. Onesuch embodiment is now described with reference to FIG. 3. Again, theone-sided entry of the coupler 104 and probe 103 beams allows for densepacking of the single-elements in arrays and leaves the activemeasurement volume/surface unobstructed to the incident RF/microwaveradiation to be measured or imaged. For lower-density arrays, a grid ofindividual single-sided elements such as those shown in FIGS. 1 and 3may be employed within the scope of the present invention.

FIG. 3 shows a microwave imaging array designated generally by numeral300. Microwave imaging array 300 consists of single-sided coupling ofindividual vapor-cell sensor elements 302 arranged in a linear or areal(two-dimensional) array. Optical coupler 304 and probe 306 EIT beams aresplit from each other using dichroic mirrors 308. Laser-beam arrays 310are derived from large-diameter laser beams 312 that are passed throughan array of micro-lenses (ML array) 314. Micro-lens arrays arecommercially available. The laser-beam arrays are matched with a planararray of sub-cells 316 containing an atomic vapor (layer thickness onthe order of a fraction of the RF wavelength of interest, with asub-cell period less than 1 mm). A dielectric coating 318 on thevapor-cell array reflects the 780-nm probe laser beam and transmits the480-nm coupler and the microwave field. The probe-beam image reflectedby the polarizing beam splitter contains the microwave information. Itis recorded using a CCD camera 320 and analyzed with an image processor322. A polarizing beam splitter (PBS) 324 is also shown.

Cavity-Enhanced Field Sensitivity

A concept of hybrid atomic detectors, as defined above, for RFdetection, in which an atomic Rydberg vapor is integrated with differentresonant materials or structures to condition the RF field of interest,is now presented. Hybrid atomic detectors in accordance with the presentinvention may advantageously achieve detection capabilities.

Near-field effects are well-known to generate regions of enhancedelectric fields. The foregoing concept of hybrid atomic detectors,described for the first time in accordance with the present invention,may be used advantageously, for instance, in plasmonic resonances innano-particles. One example of a hybrid atomic detector in accordancewith the present invention employs a split-ring resonator. A simplenear-field field enhancement device is a metal tip of sub-wavelengthdiameter. The tip enhances an RF electric field, akin to a lightning rodthat enhances the electric field near the rod in a thunderstorm. FIG. 4Ashows a calculation of the RF-field enhancement factor along the axis ofa tip 401 of 125 um diameter for several frequencies. The illustrationand plot shows that a simple structure such as a metal tip integratedinto an atomic vapor cell can enhance the field by about a factor ofthree, corresponding to 9.5 dB in intensity. For enhancement, it isimportant that the tip diameter exceeds the skin depth depicted in FIG.4B, which for cases of interest (Cr, Beryllium-Copper, etc.) is on theorder of lum in the 10 to 100 GHz range (and which scales as1/frequency^(0.5)). It follows that hybrid devices such as metal tipsimplanted into atomic vapor cells enhance the field sensitivity vialocalized near-field enhancement.

Cavity structures that are resonant with an RF field provide anothermeans for local enhancement of the field. A cavity structure can readilyprovide added control over RF field parameters such as RF fieldpolarization and frequency. Within the scope of the present invention,cavities may be engineered to reduce field inhomogeneity in an atom-RFfield interaction volume, which can be desirable in applications and isdifficult to achieve when exploiting near-field effects with tip-likestructures.

The novel concept of a hybrid atom cavity structure employed for RydbergEIT sensing is now described with reference to FIGS. 5A and 5B where anexemplary type of hybrid atom-cavity structure, designated generally bynumeral 500, and its operating principle for RF field enhancement, areshown. The structure 500 consists of two solid metal frames 502, whichmay also be referred to herein as “electrodes,” separated by a gap 504at the front of a rubidium vapor cell 506. Referring to FIG. 5B, the gap504 between the two metal frames 502 forms a cavity 510 that resonantlycouples to an impinging RF field 508, compressing a corresponding RFelectric field 512 locally within the cavity volume. The word “cavity,”is used herein in a general sense, to refer to any structure thatimposes boundary conditions of any sort on solutions to Maxwell'sequations over a specified spatial volume. A “cavity” may also bereferred to synonymously herein as a “resonator” or as “resonantstructure”

A Rydberg-atom vapor inside cavity 510 is optically interrogated formeasurements of the field 512. FIG. 6 shows a calculation of the fieldenhancement provided by the hybrid atom-cavity structure 500 withtraditionally machined electrodes inside a rubidium vapor cell, shownand described with reference to FIGS. 5A and 5B and FIGS. 7A-7D. Thestructure 500 has a gap size of 460 um that locally enhances theelectric field 512 of 4-GHz microwaves linearly polarized along Y(vertical direction in FIG. 5B) by about a factor of 10 within the gap504, corresponding to 20 dB in intensity. With EIT laser beam waists inthe range of 50 to 100 microns, the enhanced electric field remainsquite homogeneous within an active measurement volume inside ameasurement channel with dimensions on the order of 0.46×0.5×9 mm. The 9mm-long “cavity channel” (a term used herein as synonymous with both“gap” and “cavity”) provides a sufficiently long interaction volume forhigher optical absorption during measurement, and also advantageouslyprovides improved signal-to-noise in the EIT spectra.

A hybrid atom-resonator device, designated generally by numeral 700, isnow described with reference to FIGS. 7A-7D in accordance with anembodiment of the present invention. A perspective view, shown in FIG.7A, highlights spectroscopic cell 702 (otherwise referred to as “atomicvapor capsule” of “vapor capsule”) with internal structure correspondingto Stark tuner/compressor 704. FIG. 7B is a top view of the hybridatom-resonator device 700. The side view in FIG. 7C shows top electrode706 and bottom electrode 707 separated by spacer 708 to form gap 710,also referred to as a “cavity.” The perspective view of hybridatom-resonator device 700 depicted in FIG. 7D shows electrode wire leads712 coupled via electrode connections 714 into vapor capsule 702.

To demonstrate field enhancement with a hybrid atom-cavity device forhigh-sensitivity atom-based RF field measurements, the hybridatom-resonator device 700 of FIGS. 7A-7D may be deployed in theexperimental setup shown in FIG. 8A. The RF field in the cavity 710 ismeasured using Rydberg EIT as a high-efficiency non-destructive opticalprobe of field-induced level shifts of high-lying Rydberg states of ⁸⁵Rbatoms within the cavity 710. The relevant rubidium Rydberg EITenergy-level diagram in shown in the inset of FIG. 8B. Two laser beamswith λ=780 nm (720) and 480 nm (722) are counterpropagating andoverlapped through the center of the cavity 710 as illustrated in FIGS.5B and 8A. In an exemplary embodiment of the present invention, the 780nm beam 720 is focused to a half-width of 70 micron at the center of thecell 702 and has a power of 8 μW, while the 480 nm beam 722 is focusedto a half-width of 70 micron and has a power of 40 mW. Rydberg EITspectroscopy is performed by monitoring the 780 nm transmission throughthe vapor with the laser frequency stabilized to the ⁸⁵Rb 5S_(1/2)(F=3)to 5P3/2(F=4) transition while the frequency of the 480nm laser isscanned linearly across a chosen Rydberg level at a repetition rate of afew Hz. An optical frequency reference is derived from the 480 nm laserbeam 720 to calibrate the Rydberg EIT spectra.

For improved signal-to-noise in the EIT spectra, modulation spectroscopymay be implemented, in accordance with an embodiment of the presentinvention. As used herein, modulation encompasses any of frequency-,amplitude-, and step-modulation, or combinations thereof. For example,the 480 nm beam 720 may be amplitude modulated with a ˜20 kHz squarepulse at a 50/50 duty cycle and a 780 nm signal 730 derived by detectionof the 780 nm beam with a photodetector 732 may be demodulated, using alock-in amplifier (not shown) for example. The hybrid atom-cavitystructure 700 is maintained at an ambient temperature of about 45° C.for increased rubidium vapor density and 780 nm absorption. The twoelectrodes 706 and 707 forming the cavity 710 are both electricallycoupled outside the cell 702 to ground. In one example, RF fields aregenerated using a signal generator amplified by 20 dB feeding into aWR229 open-ended waveguide (2.577 to 5.154 GHz) 735 (otherwise referredto herein as a “guide.” The measurement channel/cavity 710, with theRydberg EIT laser beams 720, 722 passing though, is placed approximately1 cm away from the front face of the guide 735. In the example shown,the RF and optical beams are linearly polarized, with polarizationsdirected in parallel along the short axis (Y) of the cavity 710.

FIG. 9A shows the relative 31S Rydberg EIT spectral line shift as afunction of RF/microwave frequency for a fixed −10 dBm of injectedmicrowave power. The 31S Rydberg level is chosen such that for the 2.5to 5.2 GHz microwave frequency range spanned in the experiment, theapplied microwaves are far-off-resonance from any Rydberg transition,and the 31S state exhibits an AC-Stark shift proportional to themicrowave electric-field amplitude. At the far left of the plot shown inFIG. 9A, the laser frequency axis is centered on the 31S line with anapplied 2.5-GHz microwave field. For increasing microwave frequency, the31S level begins to substantially shift around 3.5 GHz into a largemicrowave-cavity-induced field resonance at 4.35 GHz (4.37+/−0.01 GHz inhigher-resolution scans, not shown here). Other features are evident inthe spectra, including a prominent resonance at 4.85 GHz. Multipleresonances are not unexpected from this device due to the complexity ofthe bulk cavity structure (e.g., three holes 740 (shown in FIG. 7B)containing alumina rods for electrode/cavity alignment, and longelectrode wires 712 at the back of each electrode 706, 707.

FIG. 9B plots a calculated Stark map centered on the 31S_(1/2) Rydbergstate for an applied root-mean-square (RMS) electric field E_(RMS). FIG.9C plots microwave E_(RMS) versus frequency obtained using FIGS. 9A and9B, while FIG. 9D plots measured EIT lines for 2.5 (trace 902) and 4.35GHz (trace 904) microwaves, respectively.

The example discussed herein illustrates the adaptability, as a matterof design choice by persons skilled in the art, of the geometry ofhybrid devices for high electric-field measurement sensitivity atdesired application-specific RF/microwave frequencies. In this example,microwave electric field amplitudes are obtained by fitting themicrowave-induced AC-Stark-shifted lines measured spectroscopically toGaussian functions and converting the peak frequency shifts to electricfield values using calculated Stark shifts of the rubidium 31S Rydbergstate. FIG. 9B shows a calculated Stark map centered on the field-free31S_(1/2) Rydberg state for an applied electric field. FIG. 9C shows theresulting microwave electric field measured inside the cavity as afunction of microwave frequency. At the 4.35+/−0.05 GHz resonance, acavity-enhanced microwave field E_(RMS)=13.5 V/cm was measured with arelative uncertainty <0.3 V/cm, given by the <0.1 MHz fittinguncertainty of the peak positions.

In FIG. 9A, the EIT linewidth increases from 21.7 MHz at 2.5 GHz to 84.0MHz at 4.35 GHz (see also FIG. 9D). This increase is attributed to fieldinhomogeneities in the measurement volume, which occur because the EITbeams 720, 722 and the cavity channel 710 are comparable in size, andnear-field effects at the cavity edges are sampled by the optical beams.The edges and corners at the ends of the 9-mm long cavity channel 710,where the EIT beams enter and exit the cavity in the atomic vapor, mayalso contribute. For measurement applications requiring narrowerspectroscopic line widths, inhomogeneous field broadening may bemitigated by implementing cavity structures with larger cavity volumesand/or by using smaller beam sizes for more spatially-localizedmeasurements.

To estimate the cavity enhancement factor for the electric field, acavity-enhanced 4.35 GHz field measurement described above withreference to FIGS. 9A-9D may be compared to the field measured outsideof the cavity 710. For this, the EIT beams 720, 722 are moved by Δz=−0.9mm towards the front of the vapor cell 702 and waveguide 735 from thecenter of the cavity 710. To obtain a measurable line shift at thisposition outside of the cavity, the injected microwave power isincreased from −10 to −5 dBm. This is a factor of 3.16 higher in power(and 1.78× higher in field) compared to that used in the discussion ofFIGS. 9A-9D. Under these conditions, a 4.35 GHz microwave-field-inducedAC-Stark shift of −3.80 MHz is measured, corresponding to anE_(RMS)=1.47 V/cm. Using this value for the RF field outside of thecavity, accounting for the increased injected power and neglecting thechange in field emitted from the waveguide over the small Δz(|Δz|/d=0.03«1, where |Δz|=0.9 mm is the beam position relative to thecavity and d=29.1 mm is the short axis of the waveguide), a cavityfield-enhancement factor of 13.5 V/cm/1.47/1.78 V/cm=16.3 is obtainedequivalent to a 24 dB increase in 1.47/1.78 V/cm sensitivity.

Simulations are discussed below with reference to FIG. 12, simulatingthe field inside the hybrid atom-cavity structure for an incident 4.37GHz microwave field with an amplitude of 1 V/m that is linearlypolarized along y. This simulation yields an enhancement factor of 18.6,which is about 14% higher than the measured value for 4.35 GHz fields.The difference may be explained by the 0.02 GHz difference in frequencybetween the measured and simulated fields. The simulations do notaccount for microwave losses due to the dielectric cell 702 that dependon the exact cell geometry including wall dimensions and materialdielectric constant for the microwave frequencies of interest.

In a complementary implementation of a hybrid device, instead ofinserting resonant structures 510 into a cell containing the atomicvapor, an atomic vapor may also be incorporated within a resonantstructure, within the scope of the present invention. This may bedesirable, for example, in applications where the atomic measurementneeds to be incorporated into existing RF systems (horn receivers,waveguides, etc.) for absolute leveling of RF power and field. As anexample, a sensing element 100 discussed with reference to FIG. 1, asimilar narrow dielectric capsule 232 containing an atomic vapor, couldbe incorporated within the measurement channel 710 of a resonantstructure 510 like the one shown in FIGS. 5A-5B or 7A-7D. Within thescope of the present invention, resonant structure 510 may be any typeof RF resonator or component.

Another implementation, within the scope of the present invention,having a vapor cell 1002 inside a waveguide 1004 is now described withreference to FIGS. 10A and 10B wherein, respectively, side and end viewsof a field measurement system designated generally by numeral 1000 areshown. A hole 1006 in the waveguide 1004 provides for passage of EITcoupler 1008 and probe 1010 beams. This system has been used forhigh-intensity field measurements inside the waveguide. Such a hybridsystem may be advantageously inserted into an existing RF circuit forabsolute leveling of the power through the circuit. A hybrid deviceincorporating an atomic vapor in a horn, diode, waveguide structure, orcoaxial cable, as examples, provides a versatile compact internal modulefor measurement, calibration, or power leveling etc. in microwavesources, transmission systems and other instruments in land, sea, airand space-based applications.

The absolute sensitivity achievable using a hybrid atom-resonator device700 as described herein may be tailored and further increased byimplementing Rydberg levels with higher principal and/or orbital quantumnumbers, as well as Rydberg states that are resonantly coupled to thecavity-enhanced RF field, all within the design capacity of a person ofordinary skill in the art. All such enhancements are within the scope ofthe present invention. The field enhancement and sensitivity may befurther customized, for example, by engineering the hybrid devices withresonant structures other than those heretofore described and withmetamaterials that are known in the art or discovered in the future.Complementary implementations in which the atomic vapor is incorporatedwithin a resonant structure, also within the scope of the presentinvention, may be of particular advantage when integrating an atomicmeasurement capability into existing RF systems (horn receivers,waveguides, etc.) and DC circuits/components.

Polarization Selectivity in a Hybrid System

Another feature of hybrid devices like the one described above is theirability to discriminate between different RF/microwave polarizations toachieve polarization-sensitive atom-based field measurements. For thecavity structure shown in FIGS. 5A-5B and 7A-7D, the cavity 710 acts asa RF-polarization filter in which only RF fields with a linearpolarization component along the cavity axis Y are coupled into thecavity and field-enhanced within the active measurement volume.

FIG. 11A shows experimental 31S Rydberg AC-Stark shifts as a function ofapplied microwave frequency at a fixed injected power for differentangular positions ⊖ of the microwave field polarization vector relativeto vertical (Y axis). This is done by rotating the waveguide 735 (shownin FIG. 8A) in the XY-plane counter-clockwise about the Z axis from ⊖=0°(short waveguide axis along Y) to 90° degrees (short axis of waveguidealong X) in 10° steps. At ⊖=0°, the microwave polarization is alignedwith the cavity axis of cavity 710 for maximal coupling into the cavity,as evident from curve 1102 shown in FIG. 11A. As ⊖ increases, the signaldecreases as the linear (⊖=0°) component of the microwave field parallelto the cavity axis decreases. FIG. 10B plots microwave electric field at4.35 GHz (obtained from the 31S line shifts and calculated Stark map asdescribed previously) as a function of ⊖ for the data shown in FIG. 10A.As ⊖ is increased, the field decreases because the ⊖=0°-component of themicrowave field vector (the component that couples into the resonance)decreases with a cos ⊖-dependence. A cosine-fit to the data, given bythe dashed curve 1110 in FIG. 10B, confirms this expectation, though the4.35 GHz field in the cavity does not reach zero at ⊖=90° due to cavityimperfections such as slight electrode misalignment and surface quality.It follows that the power of a linearly-polarized, resonantelectromagnetic wave coupled into the resonator and detected by theatoms within the resonator gap has a cos² ⊖-dependence, where ⊖ is themicrowave polarization angle defined above. It is therefore seen thatsuch cavity resonators emulate the functionality of an integratedmicrowave polarizer.

DC Field Tuning Capability Utilizing Electrode-Integrated Vapor Cells

A major limitation of Rydberg-atom-based measurements of weak RF fieldsis that they generally require the RF field to be resonant withdipole-allowed Rydberg transitions, which afford large electric dipolemoments and a strong atomic response to electric fields. Consequently,weak-field measurements can only be made for discrete sets of RFfrequencies that are resonant with one of the finite number of discretetransitions within a given atom. To overcome this limitation, it isdesirable to tune atomic level energies and transitions using externalfields into or near resonance with the RF field of interest to affordsufficient atomic sensitivity for a measurement. Hybrid atom-resonators,suggested for the first time in accordance with the present invention,provide a practical means to apply local fields to the atoms usingcavity/antenna/electrode structures themselves for this purpose.

Using the hybrid atom-resonator 700 described above, and in accordancewith further embodiments of the present invention, the same electrodesdescribed above in the context of RF-field enhancement are used,simultaneously or separately, to apply DC electric fields to Stark-tuneRydberg transition frequencies into resonance with weak RF fields. FIGS.13A and 13B show experimental and calculated DC Stark maps,respectively, of the 30D Rydberg state for an applied DC electric field.Note, the Stark maps are symmetric about zero field. The experimentalspectral map in FIG. 13A is obtained using the cavity by grounding oneelectrode and applying a voltage on the other electrode to generate a DCfield within the measurement channel 710 (shown in FIG. 5B). The map ofFIG. 13A shows the three |mj|=0.5, 1.5, 2.5 sublevels of the j=2.5 finestructure component and both |mj|=0.5, 1.5 sublevels of the j=1.5fine-structure component. With zero field and linearly polarized opticalbeams, the rubidium EIT ladder scheme illustrated in FIG. 5B opticallyexcites |mj|=0.5 and 1.5 Rydberg sublevels due to m-mixing by the 5P3/2hyperfine structure. The appearance of the weak j=2.5, |mj|=2.5 Rydberglevel in the experimental spectrum may be due to slight misalignments orellipticity of the optical-beam polarizations.

FIGS. 13A and 13B provide a demonstration of tuning Rydberg levels andtransitions using DC electric fields in a hybrid atom-cavity or similarstructure with electrodes integrated with an atomic vapor or gas. As anexample, a two-RF-photon transition between the 30D_(5/2) and 30D_(3/2)mj=1.5 levels may be considered. With an electric field of 0 V/cmapplied, this amounts to a transition that is resonant at ˜540 MHz, andthat is dipole allowed in second order using two ˜270 MHz RF photons. Atan electric field of +/−10V/cm, the energy difference between the statesincreases to ˜h*700 MHz (where h is the Planck constant in appropriateunits), and the transition that is dipole-allowed using two ˜350 MHz RFphotons. By application of a DC field from 0 to +/−10 V/cm, one cancontinuously tune the transition to be resonant with RF photons anywherebetween ˜270 and 350 MHz. The range of tunability can be extended,within the scope of the present invention, using, for example, higherfield values, different atomic states with different polarizabilitiesand electric dipole moments, and multi-photon excitation processes.

AC-Stark-Tuning Using External Electrodes

Continuous-frequency measurements of weak Ka-band microwave electricfields can similarly be accomplished by AC-Stark-tuning Rydbergtransitions using low-frequency RF applied with internal or externaltuning electrodes, both as described above. In one embodiment of theinvention, an AC-Stark-tuning 100 MHz RF field is applied to a vaporcell using external electrodes to Stark-tune the transition intoresonance with microwaves off-resonant from the RF-field-freetransition. FIG. 14 shows calculated Floquet spectral maps for both the47S state (1401) and 47P state (1403) modulated by the 100 MHz RF field.The 47S and 47P maps are overlaid and referenced to the same zero-fieldfrequency to show the RF-induced differential shift of the 47S1/2 to47P3/2 transition. Thus, it may anticipated that from 0 to 200 V/cm ofapplied 100 MHz RF the resonant microwave transition is continuouslytuned down by about 200 MHz.

An RF intensity and electric field calibration on the 47S state is shownin FIG. 15, mapping incident RF power to shifting of the 47S state atdifferent Stark detunings of the excitation beam. The experimental andcalculated maps are in excellent agreement, yielding a dBI to dBmconversion of dBI=dBm+50.5 and electric (E₀) field calibration usingI=I₀*10^(dBI/10)=½ϵc E₀ ², where I₀=1 W/m², ϵ is the free-spacepermittivity, and c the speed of light. The calibration in FIG. 15 isthen employed to set the RF electric field for a desired differentialshift of the 47S to 47P transition (curve 1405 in FIG. 14) at which theK_(a)-band microwaves are tuned into resonance.

Avoided crossings have been used in the interpretation of electric-fieldinduced l-mixing population in high-l states, as reported, for example,by Zhang et al., “Stark-induced L-mixing interferences in ultracoldcesium Rydberg atoms,” Phys. Rev. A, vol. 87, 033405 (2013). In FIG. 16,measured EIT spectra of the 47S state versus microwave frequencydetuning from 37.51663492 GHz (RF-free transition frequency) at a fixed−14 dBI microwave intensity (separate calibration) for 4 differentinjected RF powers/field strengths in the cell. With no RF applied (topplot in FIG. 16), the 47S line exhibits the expected Autler-Townesbehavior as the microwave frequency is scanned across the RF-field-freeresonant transition. The center of the avoided crossing lies at 0 MHzdetuning, where the Autler-Townes-split peaks are split symmetrically.As the RF power/field is increased (lower plots in the figure), theavoided crossing shifts to greater microwave detunings, tracking theAC-Stark-tuned transition frequency. At an applied −38.2 dBm of RF(bottom plot in FIG. 16) the microwaves are resonant with the transitionat a detuning of about 60 MHz.

In FIG. 17 the center of the measured avoided crossing is plotted as afunction of applied RF electric field for a series of values out toabout 200 V/cm. Uncertainty bars are set to the approximate EITlinewidth of +/−10 MHz. The calculated differential shift shown in FIG.14 is plotted here again by curve 1701 for comparison with theexperimental shift. The match between experiment and calculations isexcellent over nearly the entire range, with the measured AC-Stark-shiftexhibiting the expected quadratic dependence on the applied RF field. Atthe highest RF fields, couplings between modulated side bands of the 47Sand 47P states along with variations in the atom-microwave-fieldcoupling strength, make it difficult to discern the center of theavoided crossings in the spectra under certain experimental conditions(large optical Rabi frequencies and EIT line widths), leading todeviations between the plotted measured and calculated values.Continuous AC-Stark tuning beyond the ˜200 MHz microwave detuningmeasured here is possible, where transitions between modulated sidebands and other Floquet states in strong fields may also be used.

It is to be understood that, within the scope of the present invention,AC-Stark tuning may also use electrodes in the sensing element butexternal to the vapor cell for continuous-frequency microwave electricfield measurements.

Integrated Split-Ring Resonators

One example of a field-conditioning structure, within the scope of thepresent invention, is provided by split-ring resonators 1801, describedwith reference to FIGS. 18A-18D. Split-ring resonators 1801 are simpleresonant structures commonly used for metamaterials in the microwave,mm-wave fields, and THz regions of the electromagnetic spectrum.Split-ring field amplifiers share conceptual similarities with plasmonicresonances of microspheres used in the optical and infrared spectralranges for spectroscopy and light harvesting applications. Atomic vaporcells in quantum RF sensing elements that have integrated split-ringstructures engineered to achieve low-noise field amplification, highsensitivities, and polarization selectivity in atom-based RFelectric-field sensing applications constitute another embodiment ofatom-cavity structures for advanced sensing capabilities.

FIG. 18A illustrates the structure of one basic type of split-ringstructure: a tubular ring with a single slit. At resonance, an electricfield of an incident mm-wave field 1803 becomes compressed at a slit (or“gap”) 1805. The gap 1805 also defines the measurement channel 710 wherethe atomic vapor is optically probed for a measurement of the amplifiedfield. This operating principle is illustrated in FIG. 18b for aslit/gap with dimensions of 1×0.2×0.2 mm for the split-ring shown in theinset, and a vertically polarized microwave field incident on the cavityfrom the right. In FIG. 18a , we plot the simulated electric field valueinside the slit of this resonator type for three different gap sizes andgeometries as a function of incident microwave field frequency (fixed1V/m incident field amplitude). These split-rings exhibit resonances at14, 44, and 54 GHz, with field amplification factors of 46.8×, 74.1×,and 27.3×, respectively. The resonance frequencies can be engineeredwith simple geometrical parameters of the split-rings. In FIGS. 18C and18D, simulated resonance behaviors of other split-ring resonatorstructures are plotted, including square tubular structures, whichprovide amplification at 42.5, 125, and 94 GHz, with respectiveamplification factors of 81.9×, 12.5×, and 9.4×. These amplificationfactors correspond to intrinsic, non-electronic gains ranging from about20 dB to 35 dB. Using 1 mV/m as an upper limit to the target fieldmeasurement sensitivity without amplification, a hybrid device affording81.9× field amplification of 42.5 GHz microwaves could achieve aneffective sensitivity at the 0.01 mV/m level (for the incident field).

Other split-ring resonator structures as well as other types ofresonators, such as concentric high-Q microwave cavities, applied tofield enhancement in vapor cells are within the scope of the presentinvention.

Non-Contact Optical Heating of Vapor Cells for Temperature Stabilization

Contact-free, all-optical vapor cell heating, as now described withreference to FIGS. 19A-19C may be an essential component as an activevapor pressure control system for Rydberg RF sensors and hybrid-devices,for which the temperature control hardware (electronics, metal wires)must not alter the detector's RF field response. In accordance withembodiments of the present invention, one or more optically-absorbingmaterials are incorporated into the cell. The optically-absorbingmaterial is heated via absorption or inelastic scattering of an incidentlight beam, which in turn heats the atomic vapor (or solid metal) withinthe cell for higher atomic vapor densities. The atoms may be inconductive thermal contact with the optically-heated element by, forexample, using cells constructed out of IR-absorbing glass, orindirectly heated by an optically-absorbing material element that is inthermal contact with the vapor enclosure.

In addition to heating, it is important to stabilize the temperature ofthe cell during operation. This can be important when measurements areperformed in environments where external air temperatures cansignificantly alter the cell temperature. This is of concernparticularly when using small cells (on the order of mm of less), whoseatom temperatures and densities are more susceptible to environmentaltemperature fluctuations due to their smaller volumes. To address this,active stabilization may be implemented, within the scope of the presentinvention, by actively monitoring changes in the atomic vaportemperature or density via the optical absorption through the cell of asecond laser beam that is resonant with an atomic transition. Thisabsorption signal provides an active feedback to the amount of opticalheating power that is required to reach a desired temperature anddensity. Further, the cell can be thermally insulated from itsenvironment by, for example, incorporating an insulating vacuum layerbetween the optically-heated cell and the environment.

Referring to FIGS. 19A-19C, in accordance with an all-optical vapor cellheating method integrated into a Rydberg RF sensor, an IR-absorbingglass capsule is illuminated by a bright light source to raise theinside temperature, where an atomic vapor cell is located. FIGS. 19A and19B show an IR-glass capsule 1901 enclosing a 4 mm inner diameter atomicvapor cell 1903. FIG. 19C shows an all-optical heating test platform. Alight source 1905, such as a 50-Watt halogen bulb, is imaged onto thecapsule, and the temperature of the IR glass capsule 1901 is monitoredusing a temperature sensor, such as a thermistor (not shown), placed inthe IR glass capsule volume. A feedback loop between the thermistor andlight source intensity is implemented to regulate the temperature insidethe capsule, providing a stabilized operating temperature for uniformheating of an atomic vapor cell. A steady-state temperature of up to130° C., uniformly distributed within the capsule, is achieved in oneembodiment. Active temperature stabilization of the capsule temperatureat 50° C. (a typical operating temperature when using small 4 mminner-diameter Rb cells) has also been realized.

RF Phase Measurement Capability Using Modulated Laser Fields

Methods for employing a sensing element to extract the phase of an RFfield are now described. In accordance with embodiments of the presentinvention, a phase-sensitive recording of a coherent electromagneticfield on a surface may advantageously allow the reconstruction of thefield in all space. Applications of this reconstruction principle aboundand include holography in optics, radars based on interferometricschemes, such as SAR and InSAR, and far-field characterization ofantenna radiation patterns based on near-field measurements of amplitudeand phase of the field emitted by the antenna under test. In the lastapplication listed, the measurement is performed on a surface, and anear-field to far-field transformation is applied to calculate the fieldin all space.

To achieve phase sensitivity in a field measurement, a holographicmethod is typically employed. There, a reference wave interferes withthe waves emitted by the object. In the present case, the objectconsidered is an antenna under test that emits an RF field that needs tobe fully characterized. The reference wave, with a well-definedamplitude and phase, is preferably a plane RF field that interferes withthe object waves within the atomic vapor cell or hybrid atom-cavity cellstructure. Here, the cell is manufactured such that the atom-fieldinteraction volume measures less than one RF wavelength across, in anygiven direction. The atom-field interaction volume is given by theoverlap between the atomic vapor, the probe laser beam, and the couplerlaser beam. The magnitude of the coherent electric-field sum of theobject and reference mm-wave or microwave fields is then measured usingwell-established methods.

The measured magnitude depends on the phase difference between thereference and the object waves. In principle, such readings can beobtained on a surface surrounding the object. This may be achieved, forexample, by moving a vapor-cell sensor unit on a suitable grid with aspatial resolution much smaller than the RF wavelength. Thephase-sensitive electric-field values measured on the grid then allowfor a full three-dimensional reconstruction of the object wave. Toobtain the far field of an antenna under test one can use knownalgorithms for the near-field/far-field transformation. This measurementmethod can be readily extended to include full polarization sensitivityfor the electric-field vector utilizing hybrid atom-cavity structures(see above) or other spectroscopic techniques.

In RF field phase measurements, the generation of a well-characterizedreference wave presents a considerable problem. For comparison, we firstconsider optical holography. There, the reference wave typically is anexpanded, near-perfect plane-wave laser beam that interferes with theobject scatter within a layer of photographic emulsion (or an equivalentsubstance). It is well known in optical holography that the purity ofthe reference wave is important. The system should be largely free ofdiffraction rings caused by dust particles and other imperfections.Spurious reflections of the reference wave from smooth glass surfacesare an even greater problem. In the context of an RF measurement, thiscondition is very hard to meet, even when using state-of-the-artanechoic chambers. For quantitative work, it would also be importantthat the reference wave has fixed amplitude or, at least, a well-known,slowly varying amplitude function. The preparation of a defect-free RFreference wave that has a smooth amplitude behavior over a large surfacepresents a great challenge and is not always possible.

FIG. 20A schematically depicts a sensing element backend, designatedgenerally by numeral 2000, and an operating principle forphase-sensitive measurements of RF electric fields, in accordance withan embodiment of the present invention. A microwave horn 2002 (MW)stands for any antenna under test or other object wave of interest. Afiber modulator 2004, driven by RF source 2006, phase-coherentlyimprints an RF reference beat onto a coupler beam 104 sent to the atomsin the vapor cell 106. The RF reference beat replaces the reference beamthat is normally needed in phase sensitive (holographic) fieldmeasurement. The vapor cell 106 in the atom-based RF sensing element isof dimensions ˜1 mm, and is fiber-coupled to the 780 nm and 480 nm laserbeams. The single-sided fiber-coupled sensing element 100 is mounted ona sensor stick (not shown) with minimal dielectric profile. The sensingelement and stick is the only part of the detector that is actually inthe RF field. The fiber modulator and the optical phase control elementare integrated with a remote-control station (not shown) of the sensorexternal to the sensing element 100, and it includes the lasers, signalreadout electronics, and a computational unit for analysis. FIG. 20Bdepicts a quantum mechanical level scheme and optical/RF excitationpathways used in the phase-sensitive RF electric-field measurement.

To address these practical measurement needs, a solution is integratedinto the atom-based RF sensing element and measurement. The operatingprinciple is to imprint a phase-coherent RF reference onto the opticalcoupling laser beam via an electro-optic modulation technique. Using afiber-optic high-frequency modulator, which is commercially available,the coupler beam is frequency- or amplitude-modulated at a frequencyω_(RF) that is identical with the frequency of the RF field to bemeasured. In one implementation, the field frequency is chosen such thatit also is identical with half the separation between two neighboringS-type Rydberg levels. The level energies and their separations areknown to very high precision. There are many choices for suchtransitions. Further, the carrier frequency of the coupler laser beam104 is adjusted such that it is resonant with a transition 2010 to thenP_(3/2) Rydberg level in-between the S-levels. The Rydberg nP level isnot exactly at the midpoint between the two S Rydberg levels, leading todetunings Δ of the modulated coupler frequencies 2012 from the S-stateresonances. In rubidium, these detunings are on the order of 100 MHz andare typically larger than the Rabi frequencies of any of the involvedtransitions. Hence, the two-photon Rabi frequencies that describe thetransitions from 5P into nP via the absorption of one coupling laserphoton and the absorption (channel B in FIG. 20B) or the stimulatedemission (channel A in FIG. 20B) of an RF photon are given by

$\Omega_{A} = {\frac{\Omega_{5{P({n + 1})}S}\Omega_{{{RF}({n + 1})}{SnP}}}{2\Delta}\left\lbrack {\exp\left( {i\left( {\varphi_{5{P({n + 1})}S} - \varphi_{RF}} \right)} \right)} \right\rbrack}$$\Omega_{B} = {\frac{\Omega_{5{PnS}}\Omega_{RFnSnP}}{- 2\Delta}\left\lbrack {\exp\left( {i\left( {\varphi_{5{PnS}} + \varphi_{RF}} \right)} \right)} \right\rbrack}$

There, Ω_(5PnS) and Ω_(5P(n+1)S) are the Rabi frequencies of the opticalcoupler-laser transitions into the S Rydberg levels, Ω_(RF*) are theRabi frequencies of the RF transitions from the S Rydberg levels intothe nP_(3/2) Rydberg level, and φ_(RF) is the phase of the RF field.Also, φ_(5PnS) and φ_(5P(n+1)) ^(S) are the phases of the modulationsidebands of the coupling laser. Note there is an important differencein sign in front of the φ_(RF) in the above equations. Further, the RFfield amplitude E_(RF) is included in Ω_(RF*) becauseΩ_(RF*)=E_(RF)d_(*)/

, where d_(*) are the well-known RF electric-dipole transition matrixelements for the RF Rydberg-to-Rydberg transitions. The net coupling,Ω_(C), between the 5P state and the nP Rydberg state is then given bythe coherent sum of channels A and B in FIG. 20B),

${\Omega_{C} = {\frac{\Omega_{5P*S}\Omega_{{RF}*}}{2\Delta}\left\lbrack {{\exp\left( {i\left( {\varphi_{5{P({n + 1})}S} - \varphi_{RF}} \right)} \right)} - {\exp\left( {i\left( {\varphi_{5{PnS}} + \varphi_{RF}} \right)} \right)}} \right\rbrack}},$

where it has been assumed, for simplicity, that Ω_(5PnS) andΩ_(5P(n+1)S) are the same, and that both RF Rabi frequencies are thesame (both of which are true to good approximation). These assumptionsare not critical but help elucidate the math. The optical phasesφ_(5PnS) and φ_(5P(n+1)S) are well defined and are not prone to drift,because all frequency components of the modulated coupling laser beamfollow the exact same geometrical path. As a useful optical component, afour-prism phase control element or equivalent in the modulated couplerlaser beam is used to control the difference between the optical phasesφ_(5PnS) and φ_(5P(n+1)S). It is seen from the previous equation thatthe net coupling takes the form

Ω_(C)=Ω_(C0)cos(φ_(RF)+Φ)

where Ω_(C0) is a (complex) phase-independent pre-factor and Φ is anoffset phase that can be adjusted with the dispersion control element2003 in the coupler beam (in FIG. 20A, this is done by shifting theprisms unit 2005 left/right). Since the strengths of the Rydberg-EITlines observed in the spectra are generally proportional to |Ω_(C) ²|,the EIT line strength is proportional to cos²(φ_(RF)+Φ). The EIT linestrength therefore carries the phase information on the RF field. Wenote that the 5P to nP transition is forbidden; therefore, thecoupler-beam carrier (thin blue line in FIG. 24b ) does not introduce anadditional term in the analysis. In more general cases, such a termcould, of course, be included. Further, the magnitude of the pre-factorΩ_(C0) can be determined by finding the peak EIT line strength whilevarying Φ with the dispersion control element in the coupler beam. Theobtained peak value for Ω_(C) then reveals Ω_(C0), which in turn yieldsthe RF electric-field magnitude. In this way, E_(RF) and φ_(RF) can bothbe measured.

In this description, RF field phase (and amplitude) measurementcapability is accomplished by introducing an RF reference wave viaoptical frequency modulation. The novelty of this approach lies in thatit eliminates the need for an external RF reference wave by substitutingit with an optical modulation of laser beams directly applied to theatoms in the quantum RF sensing element. In practice, a reference wavecould also be introduced at the location of the sensing atoms in theatom-based RF sensing element using cell-integrated electrodes or cavitystructures (a hybrid system) as illustrated in FIGS. 5A and 5B, or byusing an external reference wave.

Modulated RF Detection in Atomic Vapor Cells

For telecommunications applications, the detection of modulated RFfields is desired. Due to the EIT response time of <100 ns, amplitudeand frequency modulations of high-frequency fields can be directlydetected using the atom-based sensing element as an RF/opticaltransducer without resorting to quantum interference. Similarly, RFphase-modulation detection follows from the phase-detection capabilitydescribed above. In the following, typical scenarios are described.

AM modulation at acoustic frequencies: Most Rydberg states in theFloquet map, at any carrier frequency between ˜100 MHz and several 100GHz, exhibit a differential dynamic dipole moment, with magnitudesranging into thousands of Debye. An EIT line on the map has a linewidthgiven by coupler and probe Rabi frequencies. For modulation purposes, amoderate probe and a large coupler Rabi frequency may be used, so as tomaintain a rapid EIT response time to the AM, and to broaden the EITline to several 10s of MHz. With the carrier RF applied to the EIT testcell, and choosing an operating point of the coupler-laser frequency onone of the inflection points of the Rydberg-EIT line, an AM of the RFsignal will lead to a direct response in the photodiode readout of theEIT sensing element. For a differential dipole moment d, the AM depth infield, dE, must be dE<h×dL/d, where dL is the EIT linewidth. Hence, therelative modulation depth dE/E<h×dL/(E d). This value may range fromseveral 10% down to 1%, depending on exact conditions and sensitivityrequirements.

In accordance with one embodiment of the invention, one may convert anacoustic signal using a microphone, linear amplifiers, and avoltage-controlled RF attenuator to produce an AM-modulated RF testfield. The EIT test signal is transmitted using an antenna or amicrowave horn. An EIT cell is used as receiver. Choosing an operatingpoint as described, the EIT probe photodiode signal is sent through aband-pass that transmits the acoustic frequency range. The detectedsignal is amplified and sent to a recording device and/or loudspeaker.Note that in this method on the receiver side (the EIT cell and theprocessing of the EIT probe laser signal) no demodulation is required.The EIT physics serves as demodulator. The same receiver principle canbe applied when detecting an AM-modulated transmission from elsewhere.Since the EIT sensor cell worked into the antenna receiver is opticallycoupled, an AM receiver based on it is highly EMI and EMP-proof and canwithstand high-voltage spikes, while constituting a sensitive AM radioreceiver under regular operating conditions. Modulation of FM fields canbe implemented in a similar fashion.

Incoherent RF Fields and RF Noise Measurement Capability

Prior to the present invention, Rydberg-EIT systems were capable ofcharacterizing only coherent RF fields, since Autler-Townes splittingrequires the interaction of coherent fields. That physical constrainthas been lifted for the first time in accordance with the presentinvention as now described. Steps in quantifying RF noise attributes inaccordance with an embodiment of the present invention are now describedwith reference to FIG. 22. In a first step 2201, predetermined Rydbergatomic energy levels or Rydberg-EIT spectra in the presence ofincoherent RF noise fields are calculated. A model of the Rydberg-EITunder the presence of noise is presented in the following sections.Measurement light is propagated 2203 in an atomic vapor cell, andspectral features of the atomic vapor are measured 2205. Measured tocalculated spectral features are compared 2207 and a matched spectrum isidentified 2209. This provides for quantifying 2211 the presence ofincoherent RF noise and attributes of the RF noise, including spectralnoise density, spectral power, electric field amplitude, polarization,RF noise fields propagation direction, and source characteristics suchas the gain of a horn antenna that may emit such RF noise.

In RF electric-field measurements with Rydberg EIT and Autler-Townes inatomic vapors, an EIT probe beam couples two atomic levels |1> and |2>,the EIT coupling beam couples level |1> to a Rydberg level |3>, and theRF field to be measured couples level |3> to another Rydberg level |4>.The Rabi frequency of the RF-driven transition, Ω_(RF), then becomesapparent in an Autler-Towns (AT) splitting of two lines, observed in theEIT spectrum, which in turn leads to the electric field via a basicatomic-physics calculation. To account for the effect of broadband RFfield noise in this type of atom-based RF electric field measurement, aquantitative description of the effects of broadband microwave noise isrequired. The situation considered may be fairly common, becausemicrowave amplifiers typically add broadband noise to the amplifier'soutput; the noise will then affect the atom-based electric fieldmeasurement.

To conform with a generic experimental test situation, in this treatmentit is assumed that both the coherent microwave signal, the amplitude ofwhich is to be measured, and the noise signal are transmitted from acommon microwave horn that is located at a distance greater than thehorn's far-field limit. The basic theory described here is sufficient tolay out the physics of the noise-induced effects. The theory can laterbe expanded to cover more general types of field geometries, opening upa wider range of uses (without adding substantially new basic-physicsinsights).

The effect of broadband noise on the Rydberg-atom system consists of twomain parts. The Rydberg levels |3> and |4>, which are populated by thecoherent sources (lasers, coherent microwave radiation), can transitioninto other Rydberg levels due to the frequency components of the noisespectrum that are resonant with transitions between Rydberg states. Thisprocess is akin to decays driven by blackbody radiation. The usualtreatment, in which the radiation field is quantized and the transitionrate is obtained from Fermi's golden rule and summing over the possiblefield polarizations and accessible final angular-momentum states needsto be modified so that it applies to a noise field that has awell-defined polarization and propagation direction (given by themicrowave horn's geometry). Also, the black-body energy density of thefield must be replaced by the situation-specific noise characteristics.At the location of the atoms, the noise has a spectral intensity, i.e. anoise intensity per frequency interval, measured in W/(m² Hz), that mayeither be known or may actually be a subject of study,

$I_{v} = {\frac{dI}{dv}{(v).}}$

To model the assumed RF field testing scenario, in which the coherentmicrowave field to be measured and the noise are applied to the atomsvia the same microwave horn, and that the atoms are located in the farfield of that horn, we quantize the field in one dimension only (thepropagation direction of the microwave fields emanating from the horn)and assume a fixed field polarization. For the noise-induced transitionrate, R_(fi), from an initial state |i> into a final state |f>, analysisindicates that

${R_{fi} = {\frac{e^{2}}{2\epsilon_{0}h^{2}c}{❘{n \cdot \left\langle {f{❘\hat{r}❘}i} \right\rangle}❘}^{2}{I_{v}\left( {❘v_{fi}❘} \right)}}},$

where n is the field-polarization unit vector and v_(fi) the transitionfrequency, (E_(f)−E_(i))/h, with E_(f) and E_(i) denoting the energiesof the initial and final Rydberg levels. These rates are in SI units andhave the unit “per atom and per second”. Note R_(if)=R_(fi). For thegiven states of interest (which, in the present case, are labeled |3>and |4>) we calculate the rates, R_(fi), for a known noise spectrumI_(ν) (|ν|).

In the assumed measurement scenario, the coherent microwave field to bemeasured drives the transition between Rydberg states |3> and |4>. Ifthe noise spectrum covers the transition |3> and |4>, the noise-inducedtransitions must be included in the Master equation in the form of twonoise-induced bi-directional decay terms with equal rates, R₃₄=R₄₃. Itfurther is necessary to include R₃₄ and R₄₃ in the coherence decay ratesof any off-diagonal density matrix elements that involve levels |3> or|4>, or both.

For transitions |3>→|f> and |4>→|f> different from the coherently driven|3>←→″4> transition, the noise drives transitions at rates per atom ofR_(f3)=R_(3f) and R_(f4)=R_(4f). Note that the noise-populated levels|f> have no coherences between each other and with any of the levels|1>-|4>, because the noise-induced transitions have a random quantumphase. Hence, all levels |f> that become populated from level |3>, dueto the noise, may be lumped into a fictive level |d>. Similarly, alllevels |f> that become populated from level |4>, are lumped into afictive level |e>. Due to electric-dipole selection rules, there is nooverlap between the levels lumped into the fictive level |d> (whichbecomes populated by the noise from |3>) and the levels lumped into thefictive level |e> (which becomes populated by the noise from |4>).

The net rates into the fictive levels are

$R_{d3} = {\sum\limits_{{f \neq 3},4}R_{f3}}$$R_{c4} = {\sum\limits_{{f \neq 3},4}R_{f4}}$

It also is R_(d3)=R_(3d) and R_(e4)=R_(4e). The noise also induces ACshifts that are calculated based on the same field quantization model,and using second-order perturbation theory. The shifts of levels |i>=|3>or |4> are found to be

${\Delta E_{i}} = {\sum\limits_{f \neq i}{\left\lbrack {\frac{e^{2}v_{fi}^{3}{❘{n \cdot \left\langle {f{❘\hat{r}❘}i} \right\rangle}❘}^{2}}{{hc}\epsilon_{0}}{\int_{v_{\min}}^{v_{\max}}{\frac{I_{v}(v)}{v^{2}\left( {v^{2} - v_{fi}^{2}} \right)}{dv}}}} \right\rbrack.\,}}$

The integration limits ν_(min) and ν_(max) are chosen wide enough thatthe entire noise spectrum is covered. Note that due to the ν_(fi) ³ termthe signs of the transition frequencies are important (as expected). TheAC shifts of levels |3> and |4> will need to be added into the Masterequation as noise-induced detuning terms. The noise-induced AC shifts ofall other Rydberg levels that are included in the model via lumping theminto the fictive levels |d> and |e> are not important.

Comparing the above three equations it is seen that the AC shifts areharder to calculate than the decays. For the decays, only transitionswith frequencies that lie within the noise band have effects, and thenoise spectral density is only required at these frequencies. Typically,only a few—sometimes even no—Rydberg-Rydberg transitions involvinglevels |3> or |4> are within the noise band. In contrast, all allowedtransitions involving levels |3> or |4>, including transitions withfrequencies outside the noise band, are in principle relevant in theequation above. Also, for each of these transitions, an integral overthe entire noise band needs to be evaluated. For transitions within thenoise band some care needs to be exercised because of the pole.

To evaluate the above equations, one requires the noise spectralintensity function, I_(ν) (ν). In many scenarios, it will be possiblefor the user to measure the power spectral density function, dP/dν, ofthe noise injected into the horn using a spectrum analyzer. Propagationequations available in textbooks then yield an equation for I_(ν) (ν),

${{I_{v}(v)} = {\frac{c\epsilon_{0} \times 59.96}{2x^{2}}{g_{L}(v)}\frac{dP}{dv}}},$

where dP/dν is inserted in units W/Hz and the distance from the horn, x,in meters. The spectral power, dP/dν, is normalized such that itintegrates to the total noise power that is injected into horn (inWatt). The linear gain for the horn, g_(L(ν)) is typically provided bythe manufacturer's specifications of the horn. The result for I_(ν) (ν)is then entered into the above equations to get the noise-induced decayrates and AC level shifts.

With results of the above equations, the four-level Master equation ofthe problem can be extended to include the effects of noise up to secondorder. The state space of the Master equation is amended by the fictive“levels” |d> and |e> that will hold the net populations, ρ_(dd) andρ_(ee), that are transferred by the noise out of the respective levels|3> and |4> (the levels coupled by the coherent microwave signal whoseelectric field is to be measured). The amended Master equation includesadditional terms in the equations for the level populations of theRydberg states |3> and |4>,

{dot over (ρ)}₃₃=(other terms)+R _(d3)(ρ_(dd)−ρ₃₃)

{dot over (ρ)}₄₄ =(other terms)+R _(e4)(ρ_(ee)−ρ₄₄)

The equations for the decay of the coherences that involve levels |3>and/or |4> also need to be amended so that they include all R_(3d)-,R_(3e)- and R₃₄-terms. The new equations for the fictive levels |d> and|e> are

ρ_(dd) =−R _(d3)(ρ_(dd)−ρ₃₃)

{dot over (ρ)}_(ee) =−R _(e4)(ρ_(ee)−ρ₄₄)

The modified Master equation includes no equations for any coherencesfor the fictive levels (the coherences involving the fictive levels arealways identical zero). After amending the standard four-level Masterequation with all these terms, it is solved using standard methodsyielding the coherence ρ₁₂ as a function of coupler-laser frequency,which is needed to extract the EIT spectrum.

The model EIT spectrum can be obtained, for instance, by computing theBeer's absorption coefficient in the medium as a function ofcoupler-laser detuning, α(Δ_(C)), for a given atomic vapor and celltemperature used. Note this involves an integral over the Maxwellvelocity distribution in the cell, because each velocity class has itsown Doppler shifts of coupler and probe beams. The ratio of input andoutput probe powers is then given by e^(−αL), where L is the celllength. It is noted that, after using all experimentally available inputand the computed atom-specific matrix elements for all noise-driventransitions, <f|r|i>, there is no fit parameter left to adjust the modelresults. This results in absolute, fit-free agreement when comparingmeasured and modeled spectra of the Rydberg-EIT-AT spectra under theinfluence of broadband noise.

Continuous-Frequency RF Electric Field Measurement Capability UsingStrong Atom-Field Interaction Regime

As the term is used herein, the term “strong atom-field interactionregime” refers to microwave fields characterized by electric fieldintensities exceeding those of an Autler-Townes regime in which atwo-level treatment suffices to describe observed spectral linesplittings. In order to measure RF electric fields in a strongatom-field interaction regime Floquet states are considered that exhibita high density of states, varying differential dynamic dipole momentsthroughout and multiple avoided crossings. Such a treatment is suggestedfor the first time in accordance with an embodiment of the presentinvention.

Plasma Diagnostic

Certain methods in accordance with embodiments of the present inventionmay be referred to as a plasma diagnostic usingelectromagnetically-induced transparency on plasma-embedded particles orplasma constituents for measurements of plasma fields, particleinteractions, and parameters. A method is described for plasma fieldmeasurements and diagnostics that employs electromagnetically inducedtransparency (EIT) or electromagnetically induced absorption (EIA) as ahigh-resolution quantum-optical probe of energy-level shifts ofplasma-embedded Rydberg atoms that serve as highly-sensitive localelectric-field sensors with a large dynamic range.

One embodiment of an EIT-based plasma diagnostic is now described withreference to FIGS. 23A-23C. Tracer particles of rubidium or anotherspecies suitable for EIT are incorporated into a plasma 2300 during itsgeneration. The tracer atoms are optically interrogated using EIT withthe EIT beams 2303 overlapped spatially with the tracer atoms within theplasma as shown. The relevant atomic level structure and Rydberg-EITconfiguration is illustrated for rubidium atoms in FIG. 23C, whichconsists of a 780 nm probe laser beam 2320 whose frequency is resonantwith the 5S1/2 to 5P3/2 D2 transition, and a counter-propagating 480 nmcoupler beam 2322 whose frequency is scanned around the 5P3/2 toRydberg-state transition. In this example, the 58S Rydberg state ischosen. The EIT beams are overlapped and focused to a beam waist tooptimize EIT signal strength and desired spatial resolution within theplasma 2300 (typically ˜100 micrometers). The probe transmission isdetected on a photodetector 2306 for readout. As the coupler beam isscanned across Rydberg-state resonances, the tracer atoms becometransparent to the probe light when the coupler frequency matches a 5Pto Rydberg-state resonance and a reduction in the probe transmission isdetected. In this way, Rydberg-EIT spectroscopy is performed on thetracer atoms within the plasma that are susceptible to the plasmaenvironment (field, particles). From the EIT spectra, information on theplasma fields and particles is then obtained from plasma-induced Rydbergline shifts and line-shape changes, which can be calculated to highprecision.

The polarizability of low-angular-momentum Rydberg states scales as ˜n⁷,where n is the principal quantum number. This strong scaling affords awide field measurement and sensitivity range for the diagnostic bytuning the coupler laser frequency to target the desired Rydberg levelfor the measurement.

In plasma science and applications, the plasma can be confined usingmagnetic fields which have a direct influence on the characteristics ofthe plasma. Further, magnetic fields arising from charge currents insideplasmas are themselves of interest. The EIT plasma diagnostic can alsobe used for measurements of plasma magnetic fields following the samemethodology. Calculated spectra of Rydberg atoms in magnetic fields aswell as spectra in combined magnetic and electric fields allow measuredEIT spectra from tracer atoms in, say, a magnetically-confined plasma tobe mapped onto its corresponding electric and or magnetic field.

In another embodiment of the diagnostic, described with reference toFIG. 23B, tracer atom bunches 2330 are generated from a cold-atom source2332, such as atoms collected in a magneto-optically trap, and injectedinto the plasma of interest using a pulsed pusher beam 2334. Similarly,a pulsed beam of hot atoms or molecules could be used. The atoms areseeded into the plasma where they can interact with the plasma and itsenvironment. The atoms are then optically interrogated using aRydberg-EIT optical probe 2336 that is overlapped spatially andtemporally with the atom bunch within the plasma. The optical probetransmission is similarly detected on a photodetector 2306 for readoutand analysis. In this configuration, a particle collector/detector 2340such as a microchannel plate (MCP) may also be integrated and used tomeasure the atom bunch flux that passes through the plasma and provideadditional information on plasma density via collision-induced lossesfrom the atom bunch as it interacts with the plasma, or similarly bydetection of charges/molecules resulting from interactions between theatoms and plasma constituents.

Atomic High Magnetic Field Sensor and Measurement Method

In accordance with further embodiments of the present invention, amethod is disclosed that underlies a new probe technology for highmagnetic field sensing and measurement.

The field measurement method described herein is based on atomicspectroscopy of a low-density atomic vapor encapsulated in a small(about 1cm diameter or less) glass cell. In the atom-based fieldmeasurement method, laser beams are used to measuremagnetic-field-induced atomic energy level shifts caused by the Zeemaneffect. In advanced implementations, we propose to also harness theexaggerated diamagnetic response of highly excited Rydberg atoms to themagnetic field in order to reach higher sensitivity in strong fields.Magnetic fields exceeding a few times 0.1T split hyperfine levels ofRydberg states into multiple Zeeman sublevels and transition from theweak-field (linear Zeeman) regime into the Paschen-Back regime. Theresultant saturated-absorption spectra exhibit lines that areconsiderably more spread out, and cross-over resonances disappearbecause of the decoupling of nuclear and electronic spins. The absoluteline positions and the relative separations between them are excellentmagnetic-field markers.

Saturation spectroscopy, depicted in FIG. 25A, is a well-known method toeliminate inhomogeneous line broadening caused by the Doppler effect. Ithas a vast range of use in science and technology, where it is requiredto obtain accurate spectroscopic information about atomic and moleculartransitions and their shifts caused by external fields. In saturationspectroscopy of alkali atoms in weak magnetic fields, the hyperfinelevels of the excited state, symbolically denoted |2> and |2> in FIG.25A, are split by less than the Doppler width, leading to multiplesaturation peaks and cross-over resonances in the probe-laser spectrumof a given Doppler-broadened absorption line. As known from textbookquantum mechanics, in magnetic fields exceeding a few times 0.1T thehyperfine levels split into multiple Zeeman sublevels and transitionfrom the weak-field (linear Zeeman) regime into the Paschen-Back regime.The resultant saturated-absorption spectra exhibit lines that areconsiderably more spread out, and cross-over resonances disappearbecause of the decoupling of nuclear and electronic spins. The absoluteline positions and the relative separations between them are excellentmagnetic-field markers.

Strong magnetic fields may be measured, in accordance with the presentinvention, using either standard saturation spectroscopy of Rydberglevels, as depicted in FIGS. 24A-24C, or else using a quantuminterference process in which two excitation pathways in a three-levelatomic structure destructively interfere and produce an increase in thetransmission of one of the utilized laser beams, as shown in FIGS.25A-25C. In the respective cases, FIG. 24A and FIG. 25A show respectivequantum level schemes for the two- and three-level systems, while FIGS.24B and 25B show coupling of electromagnetic fields into an atomic vaporcell 106. FIG. 24C plots a saturation spectrum of rubidium in a 0.7Tmagnetic field. The line positions and their relative separations revealthe magnetic field present within the spectroscopic cell.

In the spectroscopic method of EIT depicted in FIGS. 25A-25C, a quantuminterference process is used in which two excitation pathways in athree-level atomic structure destructively interfere and produce anincrease in the transmission of one of the utilized laser beams. Theresultant EIT transmission window presents a convenient optical readoutfor the atomic energy levels and their response to any external fields(here, a magnetic field). In the Rydberg-EIT cascade scheme, thetransparency is formed by a coherent superposition of the ground stateand a Rydberg state. Rydberg-EIT has been implemented in both coldatomic gases and in room-temperature vapor cells such as the onedepicted in FIG. 1.

The atomic states most relevant to saturation and EIT spectroscopy ofrubidium are the 5S_(1/2) ground, the 5P_(3/2) excited and the nS_(1/2),nD_(5/2) and nD_(3/2) Rydberg states of rubidium. In the magnetic fieldsof interest, these are all in the Paschen-Back regime of the hyperfinestructure. The intermediate state is in the (linear) Zeeman regime ofthe fine structure, while the Rydberg state typically is in thePaschen-Back regime of the fine structure. Also, the Rydberg statetypically has a strong shift due to atomic diamagnetism.

Due to their large size, Rydberg atoms are subject to large diamagneticshifts. For an S-type Rydberg state the Rydberg-state energy shift is,in atomic units,

${\Delta E_{r}} = {{m_{s}B} + {\frac{B^{2}}{8}\left\langle {{nlm}_{l}{❘{{\hat{r}}^{2}\sin^{2}\hat{\theta}}❘}{nlm}_{l}} \right\rangle}}$

where n, l, m_(l), m_(s) are principal, angular momentum, magneticorbital and spin quantum numbers, respectively. For S-states, l=m_(l)=0.The coordinates r and q are spherical coordinates of the Rydbergelectron (the magnetic field points along z). The shift consists of thespin Zeeman term (1^(st) term on right) and the diamagnetic term (2^(nd)term on right). The respective differential magnetic moments are thenegative derivatives with respect to the magnetic field B. Noting thatthe Bohr magneton is ½, in atomic units, and that the radial matrixelement scales as n⁴, the diamagnetic differential magnetic moment inBohr magnetons is n⁴ B/2. In a 1-Tesla field (4.25×10⁻⁶ in atomicunits), the diamagnetic exceeds the paramagnetic (spin) differentialdipole moment when n is larger than about 25. At n=50, which is easilyaccessible, the diamagnetic exceeds the paramagnetic differential dipolemoment by a factor of about 16. Hence, in strong magnetic fields thediamagnetic effect of Rydberg atoms affords orders of magnitude ofincrease in sensitivity to small magnetic field variations. Additionalaspects, including the role of quantum-chaotic behavior, are discussedin Ma et al., “Paschen-Back effects and Rydberg-state diamagnetism invapor-cell electromagnetically induced transparency” Phys. Rev. A., vo.95, 061804(R), (Jun. 27, 2017), incorporated herein by reference.

Steps in quantifying magnetic field attributes in accordance with anembodiment of the present invention are now described with reference toFIG. 21. In a first step 2101, predetermined Rydberg atomic energylevels or Rydberg-EIT spectra in a strong magnetic field are calculated.FM-modulated measurement light is propagated 2103 in an atomic vaporcell, and spectral features of the atomic vapor are measured 2105.Measured spectral features are compared to calculated spectral features2107 and a matched spectrum is identified 2109. This provides forquantifying magnetic field attributes 2111.

An Atom-Based Optical RF-Power/Voltage Transducer and Sensor.

Another aspect of the present invention is now described with referenceto FIGS. 26A and 26B. FIG. 26A schematically depicts a hybrid atom-basedoptical RF-power/voltage transducer and sensor, designated generally bynumeral 2600. Hybrid atom-based optical RF-power/voltage transducer andsensor 2600 employs an atomic vapor cell 2602 with integrated electrodes2604 that are embedded in an RF receiver or circuit 2608 for theconversion of RF signals of interest into intra-cell electric fieldsthat are measured optically via spectroscopy of field-sensitive atomicstates. By direct conversion of RF electrical signals to anatom-mediated optical readout, the atom-based transducer provides highbandwidth (DC to THz) absolute (atomic) measurement of electrical poweror voltage. A demonstration of such an atom-based transducer in 60 Hzelectrical signal measurement is shown in FIG. 26B and may beadvantageously employed as an RF receiver element at the base of anantenna in pick-up of microwaves. In both measurement and receivercases, the spectroscopic readout of the atomic cell is used to detectand determine the power-equivalent field of the electrical orelectromagnetic signal of interest.

FIG. 26B shows plots of readout from the atom-based optical RFpower/voltage transducer for a 60 Hz electrical signal applied to theelectrodes for six voltage levels. The optical lasers are near-resonantto a field-sensitive atomic Rydberg state and the transmission of theprobe laser through the vapor is detected. The field-equivalent power isthen determined by comparison of the detected transmission signal to theknown atomic response. From the detailed geometry of the chosenelectrodes and structure, and the electrical and thermal properties ofthe chosen materials used, the atomic detector readout may be used foran atomic calibration of the RF power/voltage.

An atom-based optical RF-power/voltage transducer and sensor, designatedgenerally by numeral 2700 and described with reference to FIGS. 27A and27B. Atom-based optical RF-power/voltage transducer and sensor 2700consists of a small, cylindrical cesium vapor cell with integratedinternal conductive plates. The conductive plates, or electrodes, are0.5 mm thick rings spaced 4 mm apart and each fused to the cell body onone of their sides and to windows on the other. As a result, the totalpath length through the cell is 5 mm. The inner and outer diameters ofthe cell are 3.4 mm and 5 mm, respectively, while the inner and outerdiameters of the electrode rings are 2 mm and 5 mm, respectively. Thus,two 0.7-mm thick ring electrodes are embedded within the vapor cell towhich external electrical connections are made.

An atomic vapor 2701 is contained within an atomic vapor-cellcompartment 2703 with a window 2705 that is transparent to optical beamsused for excitation of atoms to Rydberg states and another integratedwindow 2707 that is transparent to EM fields generated by the opticallyexcited atomic medium for extraction of the generated EM field. An EMfilter 2710 precludes transmission of Rydberg EIT probe and couplerbeams 103 and 104.

Embodiments of the invention described herein are intended to be merelyexemplary; variations and modifications will be apparent to thoseskilled in the art. All such variations and modifications are intendedto be within the scope of the present invention as defined in anyappended claims.

Additional teachings relating to the subject matter of the presentinvention may also be found in the following publications, incorporatedherein by reference:

-   -   Anderson et al., “A vapor-cell atomic sensor for radio-frequency        field detection using a polarization-selective field enhancement        resonator,” Appl. Phys. Lett., vol. 113, 073501 (2018)    -   Simons et al., “Electromagnetically Induced Transparency (EIT)        and Autler-Townes (AT) splitting in the presence of band-limited        white Gaussian noise,” J. Appl. Phys., vol. 123, 203105 (2018).

We claim:
 1. A method for sensing or measuring a first electromagneticfield, the method comprising: a. exciting, into a distribution ofRydberg states, atoms and/or molecules of a gas occupying a test volumecoextensive, at least in part, with the first electromagnetic field; b.structuring the first electromagnetic field by placing it ininterferometric relationship with at least one other electromagneticfield; c. measuring transmission, along a path traversing the testvolume, of at least one probe beam of electromagnetic radiation; and d.on the basis, at least, of the measured transmission, deriving aphysical characteristic of the first electromagnetic field.
 2. A methodin accordance with claim 1, wherein the gas is an atomic or molecularvapor.
 3. A method in accordance with claim 2, wherein atoms of theatomic vapor are chosen from a group of atoms including rubidium,cesium, alkali, and alkali earth atoms.
 4. A method in accordance withclaim 1, wherein the step of exciting atoms into a distribution ofRydberg states comprises optically exciting the atoms into adistribution of Rydberg states.
 5. A method in accordance with claim 1,wherein the step of exciting atoms into a distribution of Rydberg statescomprises at least one of electromagnetically induced transparency andelectromagnetically induced absorption.
 6. A method in accordance withclaim 1, wherein a physical characteristic of the first electromagneticfield is based, at least, on a change in a spectral feature of theatomic gas, and wherein the change in the spectral feature includesAutler-Townes splitting.
 7. A method in accordance with claim 1, whereinthe physical characteristic of the first electromagnetic field is fieldamplitude.
 8. A method in accordance with claim 1, wherein the physicalcharacteristic of the first electromagnetic field is its phase relativeto a fiducial phase.
 9. A method in accordance with claim 1, wherein thephysical characteristic of the first, monochromatic electromagneticfield is its phase relative to a fiduciary phase of an external RF fieldthat modulates one of the other electromagnetic fields.
 10. A method inaccordance with claim 1, where structuring the first electromagneticfield comprises superimposing an additional static or radio-frequencyfield to place the first electromagnetic field into resonance with anatomic transition.
 11. A method in accordance with claim 1, whereinstructuring the first electromagnetic field includes a modulated firstelectromagnetic field prior to the step of measuring.
 12. A method inaccordance with claim 11, wherein modulation is at least one offrequency-, amplitude-, and step-modulation.
 13. A method in accordancewith claim 1, wherein the first electromagnetic field is amplitude,frequency, polarization, or phase modulated.
 14. A method in accordancewith claim 1 wherein the physical characteristic of the firstelectromagnetic field is one of its time-varying electric fieldamplitude, frequency, polarization, or phase.
 15. A method in accordancewith claim 1 where the at least one other electromagnetic field isintroduced by an external RF reference wave.
 16. A method in accordancewith claim 1 where the at least one other electromagnetic field isintroduced by electrodes integrated into the test volume or cavitystructures.
 17. A method in accordance with claim 1 where an externalreference wave is introduced at the location of the atoms and/ormolecules.
 18. A method in accordance with claim 1, wherein the physicalcharacteristic is the electric-field sum of the first electromagneticfield and a reference field.
 19. The method in accordance with claim 18,wherein the magnitude of the electric-field sum of the firstelectromagnetic field and a reference field depends on the phasedifference between the reference field and the first electromagneticfield.
 20. The method in accordance with claim 18, wherein the physicalcharacteristic is a beat frequency resulting from the electric-field sumof the first electromagnetic field and a reference field.
 21. The methodin accordance with claim 1, wherein the physical characteristic is abeat frequency resulting from structuring the first electromagneticfield by placing it in interferometric relationship with at least oneother electromagnetic field.
 22. The method in accordance with claim 1,wherein the physical characteristic is a laser induced fluorescence. 23.The method in accordance with claim 2, wherein the distribution ofRydberg states is comprised of one or more Rydberg states.
 24. A sensorfor at least one of detecting and measuring a parameter characterizing afirst electromagnetic field, the sensor comprising: a. an excitationsource; b. an enclosure containing a gas of atoms and/or molecules ofwhich at least a subset may be excited by the excitation source into adistribution of Rydberg states; c. a detector, disposed to detect thetransmission of a probe beam after traversal of the gas by the probebeam; and d. a processor configured to derive a parameter characterizingthe first electromagnetic field based on the measured transmission ofthe probe beam.
 25. A sensor in accordance with claim 24, wherein thetransmission is sensitive to a phase characterizing the firstelectromagnetic field.
 26. A sensor in accordance with claim 24, whereinthe transmission is sensitive to a phase of transitions between Rydbergstates characterized by a specified Rabi frequency.
 27. A sensor inaccordance with claim 24, wherein the parameter varies continuously intime.
 28. A sensor in accordance with claim 24, wherein the gas includesa molecular vapor.
 29. A sensor in accordance with claim 24, wherein theexcitation source is specially configured to induce transitions betweenRydberg states at a specified Rabi frequency.
 30. A sensor in accordancewith claim 24, wherein the parameter of the first electromagnetic fieldis the propagation direction.
 31. A sensor in accordance with claim 24,wherein the parameter of the first electromagnetic field is at least oneof an amplitude, frequency, phase, or polarization.
 32. A sensor inaccordance with claim 24, wherein the parameter of the firstelectromagnetic field is the modulation of at least one of amplitude,frequency, phase, or polarization.
 33. A sensor in accordance with claim24, wherein the parameter of the first electromagnetic field is thephase of the first electromagnetic field relative to a fiduciary phase.34. A sensor in accordance with claim 24, further comprising a secondelectromagnetic field placed into interferometric relation with thefirst electromagnetic field.
 35. A sensor in accordance with claim 34,wherein the phase of the second electromagnetic field is introduced byan external RF reference source.
 36. A sensor in accordance with claim24, wherein the phase of the first electromagnetic field is relative toan RF modulated optical beam.
 37. A sensor in accordance with claim 24,wherein the phase of the first electromagnetic field is relative to anexternal RF reference wave.
 38. A sensor in accordance with claim 24,further comprising an RF reference wave.
 39. A sensor in accordance withclaim 24, wherein the parameter of the first electromagnetic field isthe electric-field sum of the first electromagnetic field and areference field.
 40. The sensor in accordance with claim 39, wherein themagnitude of the electric-field sum of the first electromagnetic fieldand a reference field depends on the phase difference between thereference field and the first electromagnetic field.
 41. The sensor inaccordance with claim 39, wherein the parameter of the transmission issensitive to a beat frequency resulting from the electric-field sum ofthe first electromagnetic field and a reference field.
 42. The sensor inaccordance with claim 24, wherein the transmission is sensitive to abeat frequency resulting from structuring the first electromagneticfield by placing it in interferometric relationship with at least oneother electromagnetic field.
 43. The sensor in accordance with claim 24,wherein the transmission is sensitive to a laser induced fluorescence.44. The sensor in accordance with claim 24, wherein the distribution ofRydberg states is comprised of one or more Rydberg states.
 45. A sensorin accordance with claim 24, wherein the parameter of the firstelectromagnetic field includes characteristics of the source of thefirst electromagnetic field.